No, the casino is not open while in port. Explorer docks at King's Wharf, which has a beach and a shopping area - you'll need to take a taxi, bus or water taxi to other parts of the island. There is one formal night on a 5-night cruise.
I posted some pictures of Bermuda in the Photo Gallery - go to EXPLORER OF THE SEAS PART II.
Have a great cruise!!
Explorer - Bermuda - August 2006
Explorer - Caribbean - July 2006
Voyager - Canada - September 2004
Empress - Bermuda - July 2004
Serenade - Canada - September 2003
Celebrity Cruise - Bermuda - July 2001
Monarch - Caribbean - January 1997
Sovereign - Caribbean - February 1996
Carnival Cruise - Bahamas - August 1990
The Explorer docks at King's Wharf, a/k/a the Royal Naval Dockyard. We found that the fastest way to get around was to take the ferry (it docks very close to the ship) to Hamilton, and get a taxi from there. The wait for a taxi at King's Wharf was long, but we hopped right on the ferry and then picked up a taxi right away in Hamilton.
If you get a chance, see Crystal and Fantasy Caves...they are amazing! The aquarium, though small, is also really neat and worthwhile.