$10K might get you someone else's headache. I highly doubt you'd get a JK for that price.
I hate to tell you but I spent $23K out the door for my 07 Sahara but it only had 9K miles on it.

About a year and a half ago I bought a 2007 X 2dr manual. It had about 23k miles on it. No real problems. The previous owner had put 18" Sahara wheels and tires on it (wouldn't have been my choice, but better than the steelies with slicks) and Herculined the interior. I paid about $13,500 for it. It took me a while to find it, but my patience paid off.