What's the best groundcover to use that requires no mowing and stays s

Remove the trim around the area and try a belt sander working from the wall and trying not to get to much into the bare wood.

Stays S?

Clover stays green. It's drought resistant and if you buy the micro stuff, it only grows about six inches tall. You can mow it if it's looking too weedy, but you generally don't have to.

Pachysandra: no mowing, stays green, no maintenance!

Use a succulent flowering ground cover. I've attached a photo of one that you could try, but there are many others. Just Google "succulent flowering ground cover" and you'll get many ideas. Good Luck!

My father planted Flowering Strawberry plants in our parkway( the place between the street and the sidewalk). Never mow, but put down something to keep the weeds from coming through. You can walk on it and it does just fine. It also comes in different colors. Hope this helps.