Turks and Caicos is a great choice but it's on the more expensive side. A $5k to $6k budget seems a little tight if you want to stay somewhere nice and not pinch pennies on dining and other stuff. The mandatory government taxes and fees on lodging are +20% which doesn't help. St. John is a much more budget friendly option. Rent a villa with a pool and a Jeep and tour around all the amazing beaches and enjoy cocktails in the pool when you return in the afternoon. If you do St. John, try to include a private or group charter to BVI if you can. There are a lot of worthwhile options (Soggy Dollar, The Baths, The Caves, The Indians, The Willie T, Sandy Spit, Sandy Cay, etc.).