totally a different budget level, but naturestone.com is an option we're looking into for our (front) porch.

Stained concrete? The grass carpet is inexpensive and simple to install,removing it after it's worn out is a different story. For that reason I suggest going for high quility material.

Build a deck on top of it. A new deck floor doesn't have to be that high over the old concrete - even 6" or 7" high would work, so it wouldn't be much taller than what you have now. You could box the sides in to conceal the old concrete completely, and it would look better than cheap plastic turf on old concrete.

We had an old circle concrete patio, we did pavers over it (DIY), it wasn't difficult, took a weekend to do and looks so much better than the concrete slab. Can be expensive though depending on the type and cost of the pavers used. Sometimes craigslist can have used pavers/bricks cheap.

http://www.lowes.com/creative-ideas/porch-deck-and-patio/concrete-patio-cover-up/project