replacing grass with something else

[as110]

Last year we got new lawn installed that dried and died. After I spent the entire summer and fall and this spring trying to fix it, I realize some of the spots don't need grass. For example where it is hard to get to with a lawn mower, on the slope I made a stone garden. At the side of the house we paved around the entrances. Where there was room I added flower beds and bushes. Now I am working on the front and my flower bed is expanding from the wall toward the side walk. I planted box wood beside the sidewalk (hoping to get a clipped hedge there one day) and enlarged the flower bed around the tree. I also added a decorative circle flower bed with white rocks around it and a concrete bird bath in the middle. The remaining lawn is very small now and very hard to mow at the edge of the rocks. To make the long story short, I want to get rid of all the grass but I don't want to use beach pebbles and more rocks or pavers but just plants that grow low and don't need cutting and will also resist weeds. ('cause the whole reason for all this work is to make sure that I won't have to kill myself to kill weeds when all the landscaping is done.)
I have seen only complete flower gardens with rocks and pavers but nothing that had a uniform planting in place of grass. Am I even on the right track or am I thinking up something that will look stupid?
I am in zone 5B.

[Kiril]

Your best bet is to design something that allows for a nice thick layer of mulch.