Tires always seem to be an interesting topic, with lots of facts, opinions, and speculation bandied about. So I thought I'd throw in my contribution.
For reference, I've had my GT for one year and have put 36K miles on it. That's 4 front tires and 7 rears so far. I tend to ride a lot of long distances, and a thousand mile day isn't unusual. Still, I like to play on the fun roads too, and can hold my own in the twisty stuff against much smaller "faster" bikes so I do get to use the full range of a tire's capabilities.
The GT uses standard tire sizes that are found on a lot of sport bikes (120/70-17 front and 180/55-17 rear), which means that there are a lot of choices out there from full-race tires, to sticky super-sport tires, to sport-touring tires. We'll stick with the sport-touring tires, as anything that gets <3,000 miles is useless to me (and you too, I'd imagine).
Here's what I've had so far on my GT, from worst to best:
4th - Metzeler Roadtec Z6
Handling good, traction good, wear poor at <4,600 miles.
These tires have a solid center band in the middle rear, which means there are no wear bars to check. Several GT riders have been fine at one fuel stop, then were on the cords at the next. They felt fine but the wear isn't that great and I can't trust them so I won't be running these any more.
3rd - Michelin Pilot Road 2CT
Handling great at first, traction great, wear good at 9-10K front, 7K rear (estimated).
These have a dual compound technology that gives harder rubber in the middle for wear, and softer on the sides for traction. I did notice a definite flat spot and hard shoulder transition near the end of these tires' life, which I could definitely feel when leaning into a corner. I also changed them early due to a long trip coming up. Now I do a lot of freeway riding, but still I need to be able to trust my tires to the end of their life. I'd run them again, but as they're comparatively expensive they wouldn't be my first choice.
2nd - Bridgestone BT021
Handling great, traction good, wear good at 6-7K rear (estimated).
I've run through about 2/3rds of a rear BT021 after changing in the middle of a cross-country trip. It felt fine, but I did get some small slips in the wet. The rear BT021 also has a dual compound with harder center tread, but I didn't notice the same wear patterns as the Pilot Roads. I also changed this rear early due to a another long trip, so I don't know how it would have fared over the next 1K miles. Note also that the front tread pattern is significantly different than the BT020 tires. This is supposed to account for the odd feathering wear that the front BT020's are known for. I have a new set of BT021's on the bike now, but haven't put enough miles on them yet to get a clearer picture.
1st - Avon AV55 and AV56 Storm-ST
Handling great, traction great, wear good at 12K front, 7K rear.
These are probably my favorite tires so far. They just plain work, without any fuss. They have a "reactive footprint" technology, which means you get a smaller contact patch when sitting upright for reduced wear, and a larger patch as the bike leans for better traction. No problem at all with wet or dry traction, and they felt great through to the end of their life. These are easily my favorite tires for the GT so far. Note that I did have a problem with one front tire developing a noticeable shimmy halfway through its life, but the distributor simply replaced the tire, no questions asked.
Also-ran - Metzeler ME880
I haven't ridden these tires on the GT, but a friend did for the '07 IronButt Rally as he was concerned about high mileage above all else. He said basically the same things that I've found from my LT days, that these Bias tires are hard as a rock so they wear very well, handle OK but not great, and tend to slip in the wet. I swapped his tires with new ME880s at the halfway point to be safe, but I'd say they could have easily gone the entire 11-12K miles front and rear. Note that he did have to use an odd sized rear, as they don't make a 180/55-17 rear ME880.
As for pressures, I haven't experimented too much. I usually run 36-38 front, and 42-44 rear. That seems to work fine for me.
Hope that helps.