A tree in the corner zone would be nice. Have you considered switching to a mix of native grasses that would be more hardy, if less perfect? Or turn the little square area into a gravel bed with an interesting mix of hardy sun-loving plantings...

Thanks ACM! I did not consider either of those options and will check it out. I was thinking a tree, maybe some variations of ornamental grass too and a rock...

Ditch the lawn for a cottage garden with sun-tolerant plants, groundcovers, shrubs, and beautiful flowing grasses, and a small, flowering tree in one of the areas. Set the plants, as suggested above, in attractive gravel or mulch. It takes some planning, so go to a local nursery to come up with a design. Start with some ground cover in the small patch next to the house, then work on the larger section. Once you get the hang of it, then you can tackle the bigger side area. I don't know what area you're in, but if your in a 6 and up planting zone, a designer will probably suggest that you include some exotic grasses and shrubs that have interesting shapes in wintertime.

Be prepared to turn into a Gardner!

Rusty empire, thank you so much for the suggestions! I did NOT think of a trellis and love the idea and concept you have incorporated! My zone is 6B. I live in Mass, close to Boston and the coast.

katbv, I have turned into a pretty good gardener over the years but the large lawn space is a little intimidating!! :-)

Good idea to plant a tree that will give some shade. Wait until the late fall. Dig a wide and deep hole and plant the tree just up to it's natural dirt line on its trunk. You must water in in really well and keep it watered. A Japanese maple would be an asset to your yard. They don't get too big.

Thanks leelee, I was considering japanese maples actually!

We have had a few Japanese maples (which I love) but they need very specific conditions...I don't think full sun is recommended, but you may want to speak to a local garden centre. They like dappled or afternoon shade, especially when young, protection from strong wind, well-drained, consistently moist soil, neither excessively wet nor dry and protection from late spring frosts, especially when young.