donlind has it right. We took a private taxi from STT to Red Hook for $20 per px+ tip. I can give you a contact off line. The tour of the island with the driver we used is well worth the trip. The cattle car taxis available at the airport will charge $15 per px + $2 or $3 per bag + tip. Probably about the same cost. The private taxi will pick you up at the same place as the other taxis and take you directly to the terminal when you are ready. The cattle car taxi will wait until every seat is full and make as many as 5 of more stops before you get to RH. There is a new terminal at RH with a bar. Good to know if you have to wait for the next ferry. If you like being on the water the Charlotte Amalie ferry is good. It runs rather infrequently. There are no facilities at CA. You stand in the sun on a sidewalk or sit on a bench to wait for the boat in CA. The combined taxi and ferry fare are more or less the same whether you go to CA or RH.
There are taxis waiting at the ferry dock when you get to STJ. They will be happy to drive you to the Westin. There are no beaches within walking distance of the Westin except its own man-made beach. Reviews of it have not been too good. Several beaches are within a taxi ride from the Westin which are GREAT. It may be worth your time and money to rent a jeep at least a few days to see the parts of the island that are not within the area served by taxis. Don't forget! they drive on the left side of the road. It is easy to adjust to the change. Much easier than you think it will take. Make a reservation ASAP. It is the high season.
Have a great trip.
JIM