OK, that helps a lot. The most common response you will get is for a Honda CR-V or a Toyota Rav-4. But you'll have to go all the way back to around 2003-2004 to get one of those in your price range. For the same money, you could get a larger 04 Toyota Highlander. The Honda and Toyota are fine vehicles but everybody wants one and they hold their values very well - so its hard to find a bargain or negotiate a good price.
If you want to get a younger SUV with fewer miles, consider thinking outside the usual Honda/Toyota box. My top choice for bargain or "value" would be a Suzuki XL-7. You could get an updated 2007 model for the same 9-10K price as a 04 Honda or Toyota. Another would be the Mitsubishi Outlander. A 2006 model would be comparably priced to the others.
The advantage of buying a more recent model is that there will be less wear&tear from age and the safety features will be better.
I'm a big fan of Subaru but the years available at your price range are prone to head gasket failure, so avoid Foresters for now.
I'm afraid I cannot recommend any small to mid-size SUV from Chevy (except for the Tracker made by Suzuki - but that is an old design), Ford, Dodge, or Jeep.
Check out both Consumer Reports annual auto issue in April and also read the owner's reviews under Edmunds' used cars.
Be sure to get a pre-purchase (actually pre-negotiation) inspection by your mechanic.
And good luck!