I would strongly recommend looking into some of the guest houses on the island
The prices are SIGNIFICANTLY cheaper than hotels. Personally, bermuda is an Island to explore, not one to pay through the nose to stay in a hotel and then feel obliged to stay on the same beach. There is so much to see and do that guest houses work perfectly for us.
The past 3 visits we have spent 2 weeks a time at
http://www.bermudagetaway.com/indexWC.htm
The location is perfect being a 2 minute walk from a ferry into hamilton, and only a short hope on the bike to the south shore beaches. Carole is a very welcoming yet unobtrusive host and the home and setting is truly magical. The experience will far outshine anything you can possibly hope to get from a hotel
See you there!