The main Charlotte Amalie harbor is a fine anchorage for both brief and longer time periods. Then
dinghy to the seawall inside at the Coast Guard station where all the other dinghies are tied up. A taxi is about US$10 to the airport and if you have the time and are really
cheap, the jitney buses go there for a lot less. There are major taxi waiting areas just across the street from the downtown seawall. Plus a major last minute T-shirt bazaar across from the dinghy seawall. (And free trash bins).
Lindbergh Bay is popular with extreme minimalist
budget cruisers but it is a walk to the terminal and finding a secure spot to lock your dinghy so it is not stolen is tricky. And you save what? $10 taxi fare if you anchor in Charlotte Amalie/Long Bay.