Reliable AWD car or crossover

Only one car brand comes to mind, Subaru. Good reliabillity, well built, and in your price range.

Sadly, not true on Subaru. Through at least the 2009 model year they commonly require head gasket replacements. And the latest engine, introduced in the 2011 Forester followed by the 2012 Impreza and 2013 Legacy / Outback, often consumes an excessive amount of oil (probably because they reduced the tension in the rings to reduce friction and improve fuel economy).

You'll see Subaru ranked highly elsewhere, but this is because the ranking elsewhere looks only at the first 2.5 years of ownership, not long enough.

The best in terms of long-term reliability is probably the CR-V followed by the RAV4.

Honda has fallen a lot in reliability in recent years. The RAV4 is more reliable than the CR-V and every other car mentioned. In my opinion, the RAV4 is a little more practical, rugged, spacious, and usable. The CR-V is very similar, but less spacious.

2007 is when they redesigned the CR-V for the 3rd gen, which is what I would go for. I don't like the 3rd gen RAV4 as much, but it's available with a V6 that makes it a rocket. The CR-V is a little more comfortable.