Can you put something over a concrete patio like stone or something to make it look nice with out removing the concrete?

You certainly can, infact a quick google search for 'resurface concrete patio' gave plenty of good options of just how to accomplish it.

There are do-it-yourself kits you can buy either online or possibly at a hardware store that seem easy enough. I'd link one here, but I don't think its allowed (would fall under advertising?).

I hope this helps, good luck!