I also just moved to central Texas, and am looking at the idea of using HabiTurf for some of the front yard. Developed at the Ladybird Johnson Wildflower Center (UT) it is fast growing, and drought resistant, and may be suitable for the foot traffic areas.
Good luck with your new home.

HI -- If you could get some patio blocks to fill in that area beside the garage . Seed the lawn with some E-CO grass or pea grass ,which ever would work best for your zone . For around the city equipment you could fill that with day lilies if they are for your zone or any mass plantings of flowers . Then you could add some big pots or planters for more flowers .

Thanks, Lefty47! A patio area hadn't occurred to me at all. That might be really nice!

could you change the walkway from concrete to stones?
maybe flagstone? as for plants ornamental cati could work.

also see if you can paint the front door a different color something unique

A design:

A other

I prefer adding some hardscape than painting.

Razor wire for the kids, rain chains for the lack of gutters. OK seriously! How about a little hedge of boxwood to create a mini-hedgerow along the entire walkway, then plant a layered garden inside the area up agsinst the house? Rainchains may work, but you may need to install at least one row of gutter across the front door, then hang the chains from each end to the ground. Good luck and have fun!

Cobblestones deter people from walking.

Succulents garden. Give away the "pups" to the invading kids to plant at their place and they might respect yours.

I would make the area a patio, extending it the width of the porch with stone or concrete to your liking. A large container plant or two would soften it up. Also remove the rocks around the side garden and in the middle of the yard.

If you install landscape fabric and cover with either stone or Pine needles it would help with splash up from your drip line staining your wall if the stain was caused by iron minerals in the soil I would trust a product called iron out you mix the crystals with water and apply it with a scrub brush

An inexpensive patio area would provide a nice welcome, and then you could splurge a bit more on containers that you could bring with you when you move out of the rental. Cleaning up the wall would make a big difference, as would a newly painted front door. Whether you choose to put a patio or plants under that roof line, you should plan on putting in a rain gutter (not a huge project for that length of roof) because heavy rains will be hard on plants and can make a mess of a patio (washing out the material between the pave stones).

I wonder why there is no guttering ?

As the garden around your utility boxes in front appear to be edged with field stone/ledge rock, I would continue with that along your front walk. First, power wash the stone wall starting from the bottom to prevent streaking. Lay one or two rows of stone, back fill with garden soil - about 6 inches and plant hostas/daylilies/flame grasses. Use pea stone as a mulch substitute. As you claim to be handy, get permission from the owner to install rain gutters, possibly with the owner paying for materials if you do the work. It will save the owner in the long run, as having rain from the roof directly deposited next to the foundation will eventually cause significant deterioration of the foundation. A very costly result for not doing such an inexpensive fix.
The lawn looks to be in that condition, not so much from persons walking on it, but possibly from some kind of infestation (sod webworm or chinch bug). If not treated, it will kill the whole lawn and spread to neighbouring properties. Your local garden center can help with direction and product choices.

For a affordable and fast fix I love the patio idea. Think of it as a front porch. A comfortable bench with pots of flowers. Maybe some garden art or statue (and these can go with you when you move). And YES! paint the front door!! Pull the door color into the patio/porch area. Soften the meter and box area with drought resistant perennials. Add a few stepping stones for access to the area.

I think a suggestion above to take out the concrete and install flagstone would be too difficult. It would be nice if the look of sidewalk up to the front door was wider. Maybe use a concrete stain on the existing cement and extend the look of the width by edging it with bricks or pavers. Then lots of flowers either in beds or planters or both! And yes to some kind of landscape fabric next to the stone, with some plantings, surrounded by mulch. You have a nice blank slate to work with. Keep us posted so we can see what fun things you come up with!

For the utility/kid problem maybe some tall fountain grass like this suggestion: http://www.midwestliving.com/garden/ideas/great-garden-cover-ups/?page=1

Paint the front door a fun wild color. In the flower bed area you could plant a collection of ornamental grasses, succulents or maybe even a bed of cacti or roses. It all depends on what grows well in your area. Tall stuff in back to cover the stains, Plant thickly or maybe a ground cover or some type of mulch to prevent mud from splashing on the wall. Embrace your kid traffic by making a path out of stepping stones, brick, or whatever suits your fancy where they currently travel. Plants in pots on the porch. I put my regular house plants on the front entry during the summer as long as they don't get direct sun.

I would absolutely reclaim the front yard from the kids' short-cut by planting some kind of local shrubs (that establish quickly and do not require annual pruning- maybe even a mixed hedgerow that birds would like) from the cement wall on the right along the curve of the property to the left, just to the point where continuing on the sidewalk is easier than moving onto the grass. I'd probably put up some kind of temporary wire fencing to protect the shrubs from kids cutting through/between the shrubs until they have established new growth and have filled in enough to make it difficult to cut between them (design it with appeal to the natural laziness of kids!)

It's a rental, so go easy on your pocketbook.
--River rock in the square area beside the garage -- maybe plant 3 pencil boxwoods there.
--Seed the lawn.
--I don't understand city equipment being in someone's front yard. I'd want to plant a large tree surrounded by creeping juniper there, but not sure city workers would appreciate your blocking access to their equipment.
That is all I would do. Maybe plantings on the other side of the sidewalk, but I wouldn't go that far with a rental.

We had a "river bed" planting area that might work for you. Softball+ size rocks along the walkway, and you can build planting ring around whatever you use as landscaping plants. We had some decorative grasses, which contrasted nicely with the round rock of the bed and the angular rock of the walls. WIth landscaping fabric underneath the rock, you'll eliminate the splash--and with some sloping may be able to move most of the water away from the foundation. (But I agree that gutters are needed.)

Plants in containers can move with you when you vacate, and you normally do not need HOA approval for containers, even large ones. If you do it correctly you can even plant shrubs and trees in containers

I agree with the pea gravel suggestion and if you did a patio area, you could use your containers to create a green barrier to prevent cut-through by the kids.

http://land8.com/photo/wakely510112?context=album&albumId=2025679:Album:538850

Try zoysia turf. We put in last year in Austin. It handles the drought and requires minimal mowing.

Widen the sidewalk all the way to the street. Here's an example. This will include covering over the garden next to the garage. Then remove the grass and rock in the curved sidewalk area and add plantings like the second photo with mulch around to keep the weeds down.

PAINT THE MAILBOX, DOOR. SIDELIGHT TRIM, AND 'FUNERAL URN' GARAGE LIGHTS A BRIGHTER COLOR...PLANT FLOWERS IN THE WALKWAY BARE AREA...IN COLORS WHICH COMPLEMENT THE DOOR/M'BOX AND LIGHTS...BEST ADVICE I EVER GOT AS A POOR PERSON, 'YOU CAN GO FAR WITH FLOWER SEEDS AND PAINT.' GOOD LUCK :-D

I think yours is a great job for EasyTurf - you'll have a lush, green, usable, durable lawn year-round without the maintenance costs and time. 21 of 32 NFL teams play and/or practice on our grass - so, you know it's gotta be some tough turf. Tough as it is, it's still soft and non-abrasive - feels better than real grass! If you have any questions, let me know -
Cheers!
George
http://www.houzz.com/projects/82914/Beautiful-Front-Yard

HI --- And it will still look good 100 plus years from now too !!!! It will never go away !

planting in containers, with strategic placement will help discourage unwanted foot traffic. use plants with thorns if further discouragement proves to be needed. also use pavers or larger rocks to catch roof drainage where that is a problem. for specific plant varieties check with local home store or nursery.

A hard scape rock garden would look nice and would also help with traffic and spatter drainage. I'd lay a barrier and fill it with pea gravel. I'd accent it with a few larger pretty stones and place a pretty pop of color in a planter or you could use three sizes of pottery graduating large to small. If HOA allows, Place a single pretty garden statue in one of the pots with the flowers. There are some tasteful selections and to each their own. I prefer natural tones and let the flowers lend the pop of color. I'm sure you'll do great! Good luck!

Am I too late to the party? So many good, and even professional, solutions in the comments. If you have solved your problems, I would be interested to know what you did. If not, I have but one idea, and I bring it to you from an elderly (now deceased) friend who had the problem of kids cutting across the lawn of her corner lot. Instead of going to war with the kids, she made and placed intriguing mosaic stepping stones along their shortcut. Between the stepping stones and right-corner of sidewalk, she placed two or three medium-sized container into which she planted Sweet William, Alyssum, and red clover. On the lawn side, between the stepping stones and the house, she placed a park bench and had a cement umbrella "port" installed (a handy neighbor did it for nothing) to create shade in the warmer months. The kids loved it. They looked for hidden treasures in the stepping stones and especially loved the bench. The kids, in turn, began to offer help in weeding out of "their" container gardens. Her little corner gained quite a bit of positive comments from neighbors, and became a welcome (maintenance-free) resting spot for young and old. The cost was low, the value priceless. When the house sold, after she passed away, the new owners--who made many changes, updates, and general upgrades to the house and property--left the corner as is, and had a lovely engraved plaque made and installed on the bench in honor of the lady who made welcome instead of war.

Good example of why people shouldn't paint their stone.