Bet/fold the turn. Check behind or call a donk on the river.
Checking the turn isn't too good. I wouldn't be that eager to give up on the hand yet. Even if the main villain is TPP, you're probably looking at a river bet when you check the turn if he has the likely QQ, but he WON'T raise your turn bet with it. This way you can get to the showdown for the same price if you're losing, but value bet when you're winning.

(I realize I'm generalizing and leaving out other possibilities, but my statements apply to a good majority of hands in this situation)