We loved Bermuda, and see why so many people do this cruise more than once. Even with 2.5 days in port, we didn't get to see everything we wanted and will be looking to go back. What we did see, we really liked, and we were able to do whatever we wanted thanks to a solid public transportation system in Bermuda:
Walked around Hamilton, including a trek to Fort Hamilton. There were some really great views from up there. The town itself is great, too
Took a bus to Somerset Bridge, the world's smallest drawbridge
We also went to Harbor Nights in Hamilton the first evening in port, it was pretty cool. Plenty of vendors, food, etc.
Walked around St George, and up to the unfinished church
Toured the Crystal Caves, ate at Swizzle Inn, and finished up with Bailey's Ice Cream (both were delicious)
Did a jetski tour from the tour operator at the dock (K2). Loved it, one of the highlights of the trip
Took a bus to Horseshoe Bay beach. Not too busy, but if it is, you can always walk down the beach to the coves past the far end and likely have very few people around. We stayed over there a good chunk of the day and it was pretty quiet, and had some beautiful views.