Hi Cheryl
I know you asked Marcy but if you don't mind, I have some advise.
I consider anything I don't book on the ship as "exploring on my own", so I count the tour I booked in St Maarten.
The key is to do some research on the internet before you arrive at the port. Have an idea what areas you want to visit or activities you want to do.
In the 1990s when we first started cruising, there was no internet so you had to either wander around or book an excursion with the ship. Now you can use the internet to find all kinds of information about activities, taxi rates etc.
We did some ports in Europe on our own. I had train times and rates and prepaid some museum entrance fees to avoid some lines. In one port, we simply walked around the little town and shopped but that was the plan.
The disadvantage to looking around without a guide is you don't know what you are seeing. I always prefer groups that are smaller. I hate it when the bus has to wait for that one family that is always late getting back to the bus. You end up being rushed since they have to make up the time. This does not happen as often with smaller groups.
I hope this helped.