Accessibility advice wanted for a first time cruiser

I'm taking a cruise on the Carnival Pride next month, with stops in Freeport and Half Moon Cay in the Bahamas, and in Grand Turk. What is the accessibility of the port cities? I use a mobility scooter. Are there accessible public restrooms, shops, and sightseeing near where the cruiseship docks? Recommendations for excursions that would be do-able? Any help is greatly appreciated.

Grand Turk, trolley.

Half Moon Cay is Carnival's private island and it's tendering. They generally don't allow, or take, scooters on tenders, so if you want to go off on that island, you'll need a wheelchair and you'll need some mobility. If the seas are even a bit rough, they won't allow you to tender.

Those private islands aren't really for us disabled. It's mostly beach activities like snorkling, watersports, horseback riding and things like that.

Freeport is OK, but Nassau is a lot better. If you can get to the straw market area, that's one place most people tend to go.