Kukki - here are some suggestions from my DD. They stayed at the Southhampton Fairmont for a week mid March.
Wander around St. George and the fort that is there, it is supposed to be a very pretty little town, but we didn't go there.
Go to the Swizzle Inn which is just west out of the Airport and have a rum swizzle! - Yummy!
Go to Horseshoe Bay. You can also walk all along Horseshoe Bay through South Shore Park to Long Bay which is all along the south shore. It is easy to get there by bus or by taxi from Hamliton. There is a little place to buy sandwiches and burgers at Horseshoe Bay. I don't know if the food is any good.
In the warmer weather there are lots of snorkel tours. The
snorkeling and diving is supposed to be excellent. There are also kayak tours. We just liked sitting on the beach. (May should be warmer than the weather we had in March)
You can golf - the Fairmont has a par three that is quite nice and wouldn't take all day to play.
Go to the Dockyards....Take a Ferry from Hamilton - I think it is about $4.00 per person, maybe $5 each way. That would be a good way to see the island from the water. There is a nice pub at the Dockyard - Frog and Onion - and shops and I think a glass blowing place. The night we were there it was really quiet and a gale was blowing thru!
Hamilton has shopping and Fort Hamilton but we didn't do any of that.
Elbow Beach is also supposed to be beautiful, but we didn't get there. We really just spent a lot of time on the beach / by the pool.
I am sure some people would like to rent the scooters and ride around the island but it's very dangerous.
Hope this give you some suggestions, Kukki. Don't forget to come back and give us a review.
P.S. Last time we sailed to Bermuda we arrived around 1pm (we were doing a trans Atlantic). The "sail in" through all the little islands/harbour and seeing all the different coloured homes with white roofs was so pretty. We were in Hamilton overnight and didn't leave until 1pm the next day.
I see by your itinerary that you arrive in St. George's at 8am, so make sure you are up early to watch the ship sail into the harbour - same when you leave SG's for Hamilton