For that price point you are only going to have a few good options that are going to last you without any problems. I can think of a few. A used Honda CR-V. A used Toyota RAV4. First two that come to mind.
For under $15,000 you can find a 2015 Toyota RAV4 on Truecar for under that price point.
For under $15,000 you can find a 2015/2014 Honda CRV on Truecar under that price.
Another car that will be fairly reliable but not quite much as the two above is the Subaru Forrester and Outback. I say that because while most are reliable about 10% have engine oil issues which will require you to add oil constantly when you own it. Not enough to cause a problem just additional maintainance.
For under $15,000 you can find a 2014 Subaru Forester for under that price.
Same thing goes for the Chevy Equiniox. Also fairly reliable but like the Subaru has issues occasionally (not engine, just annoyances which are easy to fix usually).
2016 Chevy Equinox for under that price point.
Best of luck.