Chiming in on Bimini, I agree you could definitely skip an excursion here. We did do an excursion, for a sunken ship snorkel, and that was tons of fun, but only a few hours. After, we decided to rent a golf cart and drive around the island a bit. You can get to a really nice...park? It has access to a beautiful beach area. Not sure there were any public restrooms or anything out there, so I don't know that I would plan a beach day there, but it was a nice little trip with fantastic views. We stopped at a few of the bars/food places on the way there and back. Overall a fun adventure.
I would definitely say we prefer Bimini over Nassau or Freeport.
If we ended up there again, I'd probably skip an excursion, and just do the golf cart again, although I probably wouldn't mind checking out Resort World.