I just did a internet search and was trying to find out how expensive $$$ it is to live in Virgin Islands, considering V I for 1 to 3 months out of the year.
I would guess, that the cost of renting (if open) a 37 ft. slip would be fairly high.
I could afford $ 700 to $ 900 +. Above $ 1,000... 'd think that it's a little too expensive for me. I don't get out much, in fact never before and want to see how fat my wallet needs to be before I make my travel plans.
I'd like to hear from cruisers that have traveled & lived there in the last few years. I heard that the retired military folks are there as well (I'm a ret. army guy).
As others have stated, you can live pretty cheaply if you choose to anchor out. Ongoing boat maintenance and repairs would be your largest budget variable that would depend on how sound your vessel is, how well you maintain systems and some shear luck!
Food will be more expensive than most places in the states. Milk is about $8/gallon. A liter of cheap rum is under $4 and is not so bad on cornflakes once you get used to it.
I keep a boat a little larger than yours in a slip and pay much less than your $700/month budget. I don't live aboard.
The mooring balls around St John are all $15/night. Assuming you are old enough to get the National Parks senior golden age pass (or something like that) mooring balls are only $5/night. St Thomas has very few legal mooring balls to rent and I would suggest just anchoring since it's free. Zanshin covered the BVI. The vast majority of the mooring balls in the BVI are owned by a company called Moor-Secure. There are private ones at the Bight, Bitter End, Saba and West End that one may be able to negotiate a longer term rate. I would just anchor.
Roosevelt Roads is only 40 miles from St Thomas unless one gets there via St Croix perhaps.
I do not know for sure that the hospital is still open, the base is closed. There is a very large marina, Peurto Del Rey, about two miles and a $5 taxi ride away.
The water from a properly functioning water maker has no taste as water should be.
Enjoy your adventure.