I returned from Bermuda a few weeks ago.
I enjoy these dive sites: (south side) : the wreck of the Hermes, the "Southwest Breakers", and Hangover Hole.
Other good dives -on the west (?) side- the wreck of the Constellation, the L'herminnie(sp??)-
Good pubs-the Hogg Penny , in Hamilton, and Henry 8ths in Southampton. There are, as with the dive sites many more for your enjoyment. (i'm nore of a diver than a "Pubber" (?)
Sites: (land) Dockyard, St. George. Hamilton, for shopping.
AFAIK "Padi and SSI" should not be a problem- as long as you both have your c-cards with you.
Weight calculations- the claim is that the salinity of the sea near Bermuda is highrer than average, so many people use a few more pounds of lead than ay other locations.
I'd also suggest arranging your diving in advance- it could be a hassle to do after you arrive.
Unless the cruise ship has made arrangements for you, be aware that getting to the shop may not be as simple as in other locations-no rental cars, cabs are a bit costly, and buses run on their schedule-not yours.
You might want to book with a shop that is near where the boat is docked. Perhaps the cruise people have an arrangement with one of the shops.
If you are in need of a recommendation, I have had great success and fun diving with
Dive Bermuda. Their shop is located at the Fairmont Southampton Hotel's beach.
Enjoy your trip.