We used to be a member at Triangle and of the places they dive, I very much like North Rock (which they don't go too often as it's quite far) and "Cathedral". The wrecks are all quite impressive though I'm not very fond of the Dredger as it is in the middle of nowhere so can be a bit dull.
Bermuda is very beautiful and the South Shore beaches are quite spectacular. Good snorkelling in Church Bay and even in Warwick Long Bay. Near Grotto Bay are many caves - you don't need to pay money to go and see Crystal Caves. Kayaking is quite nice there too. We have seen some turtles hanging around in the bay on the other side of the bridge from the hotel. Dockyard is somewhat unique in architecture though I would hesitate to call it a "must see".
Given location Swizzle Inn down the road is the obvious choice as a bar / restaurant. This is the only chain in Bermuda as far as I'm aware where they don't add tip automatically to the bill. Nearby Tom Moore's is a nice and historic but expensive restaurant, and Friday night is when people will go out to Hamilton to party. If you are there on Friday the happy hour at Hamilton Princess hotel is very popular, and you can make your way down the Front St. and bar hop. Most bars on Front St. are fine up to Docksiders which can be a little too exciting at times.
I'm not too familiar with restaurants in St. George's (the other town closer to Grotto Bay). It's a nice historic town, but food wise there are only a few pubs as far as I'm aware.
Near the Aquarium, the restaurant Rustico's is excellent and (in Bermuda) reasonably priced. Its sister restaurant the Dining Room again is very good and is located at the lighthouse near Henry VIII pub which is on the South Shore (there are two lighthouses in Bermuda). The view from this lighthouse is probably one of the best in the island, but you need to walk up quite steep hill. You can rent scooters too though I advise people not to unless they have driven it before and are comfortable with it. There is more traffic in Bermuda than people may think.
Hope this is helpful.