Maybe something like this. I would check out Ikea or the container store for living room bins and organization.

Your photos made me so happy! Oh to have a busy household once again, or to sit on the floor playing cars or barbies with the kids, I miss it all!
But I DO remember being so frustrated with all the kid stuff everywhere lol.
Here's what I think: get a hall tree kind of like the one in this photo, maybe a lighter color though and put it where everyone is hanging their backpacks etc. and what I wish I would have done but never did....enforce that they have to put their stuff in its place immediately when they come in the door.
Then, I wonder if you can turn the couch around so the part by the window would have its back facing the entryway, then remove the pretty seat you have in the entryway, and put a little console type thing there, against the back of the couch. Then under that console is where they would put their shoes and boots.
And enjoy those kids, there will come a time you'll miss the mess!

I would build a closet where you have the bench it also gives some separation and cold control from the door and maybe use the back door for family insted of this one.

I think Patricia nailed it.

We actually built a mud room around our back door. It helped with the cold air coming in and gave us space for our junk.

The bench is a perfect spot for an entry closet and it would formalize the entry.

http://www.potterybarn.com/m/products/samantha-entryway-collection/?pkey=call-entryway&isx=0.0.480
http://www.potterybarn.com/m/products/elton-fretwork-cabinet/?pkey=ccabinets&isx=0.0.660
http://www.potterybarn.com/m/products/banks-bookcase-cabinet/?pkey=ccabinets&isx=0.0.295

Hi there! If you are on a budget, look to IKEA for all your storage needs. They really are the champions of small-space organizing. In the entryway, you could maybe use their Stall shoe cabinets, combined with either a grid or continuous row of hooks to take care of entryway clutter. Make it pretty by adding a lamp, mirror...maybe artwork.

Or, you could lay a Kallax shelving unit on its side, place a cushion top to create a bench, then store shoes, dog leashes, etc. in bins in the cubbies below.

Here are some examples of basic storage made pretty:

More:

Since you have young kids, you could mount these cute little doggie hooks along a low row for their coats, then do a row of hooks for the adults' coats higher in the wall. Turn it into an art installation!

Oops, forgot to attach pics....

You could use the Stickat baskets on some of the hooks to hold mittens, hats, etc.

The area by the FP may be wide enough to hold a Kallaz unit on each side...I believe they are about 33" wide. You could get the four-cubby size, which would be about 30" high, and use the space above to hang artwork. Decorative bins and baskets hide the toys. It's not as beautiful as built-ins, but as a temporary solution until the kids are older, it is adequate. Once you have outgrown the need for the Kallax units in your living room, they will come in handy as closet organizers, or basement storage.

There are so many great ideas out there for creative uses for IKEA furniture...both on their site and on the Internet. I hope you can find something that works AND looks pretty!

More ideas:

See that bench next to your door? Putting crates under there will hold shoes. Jackets, if you can, keep in closets. You should definitely invest in a storage coffee table to hold different things. Even get a new bench, if you want, to act like a chest. A smaller door rug will make your home appear to be more open when first walking in. Consider rearranging furniture to make it seem less congested. Good Luck!

Here are some pictures:

Can you post more pictures of the other side of the Livingroom

I like the economy of the basketry solutions Karemore has found for you, but I see 15 pairs of shoes at the door: if the house rule becomes only one pair of shoes per person, will a basket per person fit by the door/sofa? (I'd give the dog one, too, for leash and baggies and gloves).

Building off auntthelmas idea is this:

http://www.apartmenttherapy.com/ikea-billy-the-worlds-most-versatile-bookcase-211402

This would be a nice side table

http://www.westelm.com/m/products/parsons-end-tables-h1426/?pkey=e|side+tables|108|best|4294967200|3|15|%2Fside-tables%2Ffurniture|15&cm_src=PRODUCTSEARCH

Because the doors hinges are only a door frame from the adjacent wall, you need to keep the area along that wall open for foot traffic. Hanging anything other than art, in thin rather than thick frames, on that wall would be a mistake. You could, however, put your bench at the very end of that wall -- well away from the door.

The bench that, as you enter the door, is on the left next to the
sofa needs to be moved elsewhere and you should put a cabinet there,
beside the sofa (facing the entry), with doors to hide the shoes put in the cabinet. You can also place a tall thin lamp with a white shade atop it in order to provide for someone wanting to sit at the sofa and read. Would not want the cabinet to be higher deeper
than the bench seat or higher than the back of the sofa or wider/longer than
the sofa arm from front to back.

http://images.crateandbarrel.com/is/image/Crate/Harrison36InBaseW2DoorsWhiteSHF16_1x1
http://www.amerheritage.com/merchimages/furniture/barnwood/jellycabinet-2door2drawer.jpg

Alternately, at the end of that wall -- well away from the door -- you could put a traditional coat rack available at any office supply store

https://www.dutchcrafters.com/product_images/pid_1725-Amish-Pine-Coat-Rack-8.jpg

perhaps with an umbrella stand beside it

http://ak1.ostkcdn.com/images/products/7873062/7873062/D-Art-Mahogany-Hardwood-Finish-Visalia-Umbrella-Stand-P15256855.jpg

or as part of it

http://photo.foter.com/photos/pi/261/coat-tree-coat-rack-umbrella-stand-coat-rack-coat-rack-tree-coat-and-ha-by-deluxecomfort-98-80-attractive-styling-compact-durable-metal-construction-gets-rid-of-cluter-portable-coat-tree-coat-rack-umb.jpg

or hall tree.

https://secure.img1.wfrcdn.com/lf/79/hash/11067/11989470/1/Sedona%2BHall%2BTree.jpg

Afterthought:

Seriously consider a pair of matching vertical cabinets on each side of the fireplace with solid doors on the bottom half for additional storage (shoes/toys) and, on the top half, either open shelves (for use as a bookcase) or glass doors for use as a curio cabinet.

http://www.cutenareta.com/wp-content/uploads/2015/10/interior-furniture-white-wooden-cabinet-with-bookcase-flanking-wall-mounted-tv-and-stone-frame-gas-fireplace-shelves-beside-fireplace.jpg