Myrtle (periwinkle) is easy, flowers, spreads, stays low to the ground. It grows wild around here. I just rip a piece with a small root out of the soil and shove it in somewhere else. Lily-of-the-valley is beautiful and aromatic but short-lived; however it will grow through the myrtle. Sweet woodruff is nice. I dislike pachysandra and English Ivy.
Another fast grower is Creeping Jenny (Lysimachia nummularia). They don’t call her “creeping Jenny” for nothing. Pretty yellow flowers bloom in the spring. I also stick some in my pot gardens – outside for the summer only. Bishop’s Weed is fast-growing and invasive.
Any kind of mint or lemon balm will also run amok.
Ginger, pulmonaria, and lamium are low-growing plants and don’t lie flat.
Myrtle would get my vote. You might want to sit on a towel however. Nothing will exactly replace grass.
Walk around the neighborhood and see what other gardners have done.