We've been to Nassau numerous times so we did not book an excursion. We ate lunch at a second floor restaurant on Bay Street. We highly recommend that you check out "where the locals eat" which include these second floor restaurants. On another trip we ate at a "local" place near Junkaroo Beach. We then walked to the Queen's Staircase. It was worth the trip and yes, there were people who imposed upon you to tell you the story of the staircase and ask (openly) for a donation but it was worth it. We skipped going in to the Fort and then we walked back downtown. We stopped at the historical society which was small but had an interesting display and then we walked back to Bay Street to the Rumcake Factory. Frankly I think they ripped us off there -- the sign said buy a medium or large and get a small free and I believe they charged us for both and they kept the detailed receipt. We briefly walked through the straw market which can be a good place to shop if you can ignore the "high pressure" and just look for what you want. There are also plenty of vendors in the plaza that you need to walk through getting on and off the pier.
If you want to do anything in Freeport, book an excursion. We were going to take the bicycle trip but due to a last minute injury we didn't sign up for it. So we took the taxi to Fort Lucaya and basically wasted two hours and $20.