Here are some more ideas as well as ones to avoid:
http://dnr.maryland.gov/wildlife/habitat/wildacres/wagroundcovers.asp

We have periwinkle/vinca and it works great. My kids run through it and it doesn't get too high. We haven't had issues with it invading or spreading too quickly (I actually wish it would spread a little faster as there are some bare patches!). It's also really pretty in the spring. It was here when we moved in, so I can't offer much advice on growing it, but we like it as ground cover.

Check out stepables.com. Lots of ideas for different conditions. We planted white clover and contained it within a stone border so it won't spread. Very hardy and feels great underfoot. Mow it every so often to cut off the flowers if you don't want bees. And be prepared for comments because most people think it's a weed. But Google "clover as lawn alternative" and you will find lots of fans.

Oh gosh no- not mint!!