Bridgestone Dueler AT Revos have been a favorite of 4Runner off roaders for use conditions you describe.
http://www.tirerack.com/tires/tires....ler+A%2FT+Revo
Once you go to 33"s, you have to start opening up the clearances as mentioned above.. The front wheel well pinch seam is already fairly close with 265/75 x 16s 31 inch tires, which I have.
Only down side when I had them, is as they wear, they can become pretty noisy on highway, which the more aggressive off road tires will do..
Replaced them with Michelin LTX, which aren't as good as the Deuler off-road, but still a good all terrain tire...