In Hamilton right on Front Street there are a few spots that serve drinks that seemed very popular. Blue Juice is the one I remember though. I will warn you, prices are high. There was one place that wanted $14 for a cheese steak.
When in St George, dont miss Tobacco Bay. It is a nice swimming spot with calm waters. The beach is not in great shape though because of the hurricane last year.
For sight seeing, buy the Heritage Pass. It will get you into about 8 places for one price including the BUEI (Bermuda Underwater Exploration Institute) and the Zoo and Aquarium. Both worth the trip.
Gibbs Hill Lighthouse has a wonderful 360 view of the whole island.
Jobsons Cove, just past Warwick Beach is ideal.. My family had the cove to ourselves last week. It was like our own private pool. We even swam with a fish.
To get around, buy the bus and ferry passes. They will take you anywhere you need to go.
Shopping, well Hamilton is all you need. There is a shop for just about anything right outside your dock.
If you want even more information, you can email me at firstname.lastname@example.org
and I will answer any more questions. I have been there twice now and hope to go back again.