Permit me to also weigh in...
In your original post, you mentioned that you're looking for places to purchase gifts to bring back home. Two suggestions:
In my opinion, the best "souvenir-style" shirts/hats/tanks are at
Sunset Beach Bar. They're very much in the style of RonJon, if you've seen those shirts. While not cheap, they will likely be worn back home because they reflect the "island vibe."
Also, a shopping trip to Philipsburg also might interest you. However, you should check the
cruise ship schedule in advance. You don't want to go when there are a lot of ships in port. However, if there are no ships in port, a lot of the shops will be closed.
As I see it, if I had limited time on the island, I would skip shopping in Philipsburg, and instead put plastic down for some shirts at Sunset Beach Bar. You can enjoy the beach, have an adult soda, and watch planes land (from there, or (as RonDon suggested), go down the beach to Tortuga, where food/drink is less expensive). Also, same as Philipsburg, keep an eye on the cruise ship schedule. A lot of ships host excursions to Sunset BB.
Here is the link to the Sunset webcam. And while the beach looks rocky now, it will be all sand by January.
Final pro-tip: Tune your rental car radio to FM 91.9. It's the station you'll want to listen to. Not only will you hear a good mix of music, restaurants advertise specials and events that might interest you. In fact, you can
listen now!!