From your mileage, age, and cost I am assuming you are willing to go very old to stay in your price point.
Going on that assumption (and assuming those are not typos) your best bet is an old Toyota. Like an old Toyota 4Runner would give you good off-road capability. The RAV4 and the CRV are light duty cars that won't take you off road like a Jeep. The 2010 4 Runner however would. That is a durable truck-based body on frame design that can give you some good offroading.
However, if you don't need that heavy-duty off-road capability that the 4Runner offers like a Jeep but with much better reliability, then the two you picked (RAV4/CRV) will work fine. 2009-2011 RAV4 has good reliablity and is in your $6000 price range, and the CRV from 2012 on has good reliablity (before that the climate control is a problem spot). You might be able to get that in your price point as well.
Since you want to keep the price very low, I would stick with Toyota's 4Runner, RAV4, and Honda's CRV and not look further. Going that old I don't get very adventurous recommending other brands because usually you are just asking for trouble (Mazda could be okay but I don't particularly like their AWD). Subaru's are good until about 100,000 miles that old unforutnately because their main engine seals back then failed a lot in about 20% of their cars). If that engine seal does not go, they can also last 200,00 easy as troublefree as Honda and Toyota, and they do have a better AWD. If you like Subaru, the Forrester can work as well the Outback taking a chance with the main engine seal.
Best of luck.