All good suggestions so far.
If you & the wife are up to it, you should also rent a scooter. Definitely the best way to see the island.
Wednesday late afternoon the city of Hamilton host Harbor Nights. Normally there will be live entertainment, and vender's selling stuff. Its always nice to walk around, and get a bite to eat at one of the near by restaurants.
When visiting Bermuda you have to get on the water. Her are my suggestions all ranging in price.
Cheapest way is by ferry, if you rented scooters you can load them on the boat, for an extra fee.
http://www.bermuda-attractions.com/bermuda_000073.htm
13ft Boston whaler rentals are always nice, as are the jetski tours
http://www.bdawatersports.com/
http://www.h2osportsbermuda.com/
If you would like some one elso to do the driving for you then book a Wildcat or Parsailing tour
http://www.kswatersports.com/WildcatTourListings.php
If you have any thing in particular you would like to know about, just shout me a pm. Enjoy your stay.