pic righted.

What zone are you in? Type of soil sandy, clay, acid, alkaline? Average annual precipitation?

For the time being, why don't you just mulch the heck out of it with some fairly chunky wood mulch? That would at least give you a uniform look while you figure out a more permanent plan and it will protect the soil.
Because right now it does look patchy and kinda h*llish. Have you walked around the neighborhood to see what other people do to keep that strip looking tidy or nice?

I'd try to figure out why grass won't grow there before I started planting other (costly) plants.

Is there a drainage issue on bottom left side? Does the area get walked on? Is the soil compacted? Too much shade?

I als do wonder what your neighbors areas look like.

I like the idea of "mulch like heck" for the time being and maybe level out the area. Let what's there die off and become a blank slate. If your county has any sort of online resource for good drought resistant plants in your area, use this time to do your plant research and maybe imagine/draw up some planting ideas.

Then plant whenever is the best time for your zone (for my zone it's the late fall/winter, in general; spring is okay and summer usually means a new plant in full sun may not make it...at least under my watch). If you don't want much maintenance, maybe consider evergreen low water groundcovers.