look at a set of goodyear wrangler authority ATs. I know some people that swear by them, but I haven't been able to find them anywhere except walmart and they only have them in the original 32s

 

I just changed my OEM tires out for Goodyear DuraTracs, keeping the original 285/75 size. They have a noticable, but not annoying hum. On pavement performance actually seems more solid than the GM OEM tires. Offroad they perform very well. While I don't do any deep mudding but they have powered easily through the mud I have encountered. The biggest downside is that they have reduced my gas mileage by about 1-2 MPG. For me the trade-offs are good and I am happy with the Dura Tracs. They also look much more like tires on an H3 oughta look.

If I wasn't going to offroad much or in very demanding situations I would consider the BFG AT-KO's for quieter pavement running and gas mileage.

 

I have a 2009 base model. I do mostly highway driving, however I love to go off road and take it on the beach when I am at the Outer Banks. On my previous vehicle I had installed the Bridgestone Duelers AT Revos. What a great tire, worked well in the rain, on sand, mud and the deep snow of Northern Ohio. Best of all no noise or hummmm. Today I pulled the trigger on another set for my H3. These are the Revo 2s. This tire has great road manners and I can't wait till I get the hummer on the beach in NC.