We have visited STX at least 6 or seven times both as a land vacation and also by bareboat. It is often overlooked as it is further away from the other Virgins but it is one of our favorites and has much to offer.
Good that you will have a car as Carambola is at the far end of the island and is somewhat remote. Feels crazy to say that when the island is only about 30 miles long! It is a lovely spot and you should enjoy your time there.
As far as eating out there are MANY good choices. Closest to you is [email]eat@canebay[/email] and they have wonderful food and a view to die for and right across from world class diving and good snorkeling as well as a pretty beach. In Christiansted our favorite is Savant and on the east end Duggan's Reef (this will be a bit of a ride for you). Frediericksted is not to be avoided in my opinion these days. I understand it was quite run down but they have the cruise ship dock there and on the ocean block there are many good and fun places to eat to watch the sunset. Also very nice beaches all along there. You can avoid crusie ship days, though many leave for excursions on other parts of the island.
Things to do: It depends what you like! A trip to Buck Island is a must for snorkeling. There are several providers from Christiansted and we love going out with Lewellyn who is a local guy (he goes out of STX YC) and does not have a website and only a phone number is 430-773-9027. A visit to the downtown boardwalk area is fun and there are some fun restaurants there as well as a walk aournd the downtown to some of the various shops that sell locally made jewelry (we love IB Designs) but there are many others (Crucian Gold and Sonya's). Also love the Jan Mitchell gallery. Went to the Domino club once and it was an experience. It is rather run down and you have to pay extra to see the pigs which only drink non-alcoholic beer. It is not too far from where you are staying and a legend in STX. Hope this is helpful. Keep an open mind and ignore the oil refinery (near the airport and you don't have to see it unless you are coming and going) and a few American fast food places frown and find the real island. We have loved our time there and find the people and expericnes we have had there to be amazing. Enjoy!