Dan, I lived in Palau for two years and that's where I got started on GT fishing. There are some sizable GTs, but you're not going to find them around Koror. You need to get down to Angaur or, even better, up north to Kayangel and the reefs north of that. But that's a trip you have to plan well ahead of time and usually the people booking that trip (Japanese) are going to Palau solely for fishing. You could also catch some decent GTs around the channels on the west side of Babeldaob (the island north of Koror).
Look at NECO Marine for diving - they are solid. Fish and Fins is, too. Don't recommend Sams - that guy is a jerk and he'll nickel and dime you wherever he can. The owner of NECO is also a really good fisherman, but I'm unsure what he offers in terms of charters. I have heard that most all of the GT charters are done through Japanese captains, but I just don't have any contact info for them.
I was in Palau last summer and heard second-hand that the guy who runs this restaurant (
http://www.palauwaterfrontvilla.com/) sets up some of the trips for the big-name Japanese guys who come down. Maybe send him an email?
Also, there is a member on here who lives in Palau. I remember seeing his post recently in the "show me your boat" thread. He'd probably be really helpful.
You'll deal with a lot of sharks in Palau, so take many lures. The locals mostly (always?) keep GTs for eating, which is why there is nothing of size anywhere that people live. I was on Angaur for a year and caught maybe a dozen GTs, fishing nearly every day. My gear wasn't heavy so I lost the only two that were biggish (50lbs.).
But yeah, Palau is really beautiful and you'll like it.