Just saw your post.
We cruised Bermuda last October. I can not help with hotel, since we live in New Jersey. If flying into Newark check airport hotels. There is a train that runs to Path train in Hoboken, which you would connect with NYC subway or just Urber or a shuttle to port.
We went to Horseshoe Bay Beach on our first day. Shuttles are right a port, $6-7 per person. The shuttle brings you down the hill from main road right to beach.
The beach is gorgeous with coves to North of where you come on that are breathtaking. The beach has everything you need, rentals, food, bar, bathroom, shower and changing area. When you want to go back to the ship the vans are lined up to go back.
The port area has a lot to do. There is the fort with the Bermuda Maritime Museum. There is also Dolphin Quest Bermuda and a Snorkel Park. Plus, a lot of water excursions leave right from that area.
There is the West End Trolley Tour of the area, plus shopping and restaurants.
On the second day we did the tour of the island, which stops at the Gibb Lighhouse, Hamilton, Saint George and a few other areas. It was a great tour, impart because our driver/tour guide was fantastic.
The water is not to be missed in Bermuda. Have a wonderful time.