So before I came down to work in the USVI, I checked around the forums here and didn't find a great deal of specifics. So, as a service to others considering the same, here is some (hopefully) useful info for the island of St Thomas:
The main travel agencies that have contracts here are World Wide and RTG. I think Titan has some too, but most people seem to be with Worldwide.
Transportation around the island: there is the safari bus, an open air pickup (many of them) with bench seats that make a big loop around the island. If you live near the safari route it makes it easy and cheap to get to the hospital. If not, you'll likely need an island car (ask around, can often be found for under $1500 and then you sell it for same when you leave) or a rental, sometimes from locals who rent to travel nurses, or a scooter. You can rent one or buy one from the scooter rental places. Dangerous, yes, but cheap on gas and easy to get around traffic. The roads are steep, narrow, and have no shoulder. So don't plan on bicycling as I originally did. Don't try and drive down town on a 5 or 6 cruise ship day, it gets jammed up!
Housing: world wide lets you find your own, I used craigs list and did fine. RTG and Titan put up most of their nurses at Saphire Beach, which is near Redhook and right on the safari route. Nice because if you go to the bar, you'll find other travel nurses to hang with. It isn't too far to most places on the island...if I could do it over again I'd be near redhook, since it it where much of the sailing and diving and such is based out of. And it is away from the cruise ships and is on the safari route. But there are other nice places too.
The people at the hospital: Nice. At least in the same ratio of nice people to grumpy pants as you're likely to find anywhere. Locals included, who are mostly nice and smiling and welcoming to travelers. Sure, there are some a little grumpy, and some a little lazy, but I have observed a similar percentage of lazy travlers as lazy locals. Most of this is a consequence of island time. Figure it out and get used to it. Nothing happens fast here. Nothing. Or effeciently. Nothing is effecient. It is comical except when it isn't. This probably isn't like where you are coming from. Just roll with it. Do your best and it'll be ok.
Money: Seems to be about the same regardless of which company you use. Neighborhood of $1300/week before housing cost. Overtime is $40/hr, sometimes available. Might be able to pick up per diem shifts at St Croix, they are hurting for staff and are trying not to use travelers, but will pay for your flight over from St Thomas and put you up in a hotel for 1-2 shifts a week. Haven't done it, but some folks here are looking at it as an option to make more money.
Other stuff: the license endoresment can take a little time. Bring hard copies of your bls, acls, pals, whatever cards. Food is expensive here. Most things are expensive here. Except rum, which is plentyful and cheap and good. Cell phones from home will work if they are GSM (like att) and not CGMA (like Verizon). Or you can buy a local prepaid tracfone for about $10 and put minutes on it as you need them. Don't arrive broke and counting on your first big pay check. Have something in the bank when you arrive, just good policy. Take it easy, don't get mad and don't be arrogant, smile, and BE SURE TO SAY "Good Morning" or "Good Day" to people or you won't get anything done. It is a formal nicety widely observed here. You don't want to be the rude continental.
Hope this helps, if you have specific questions send me a pm.