I'd try Wild Ginger (Asarum Aristolochiaceae)- but it is a slow grower, Barrenwort (Epimedium grandiflorum), Pachysandra - another slow grower or some Juniper. The Juniper won't have the density to keep out all the weeds though but a huge blanket of it sure looks cool!

Are you looking at a shade or sun area?

Come to The Middle Tennessee Plant Swap and there should be several different kinds of ground cover to choose from.

Mostly sun - I'm leaving the lawn in the front yard under our maple tree. The back yard is my target for lawn replacement.

Thanks for the ideas, I'll try them all!