With only 5 days I'd focus on locations that don't require beyond local flights. That seems to exclude Cayman Brac, Little Cayman or Grand Turk. Most have connecting flights but it burns the afternoon getting there. From your location there should be islands you can reach by noon instead.
Also places where the better diving doesn't require long boat rides - that excludes Provo as the short trips return about 2:30PM (2 dives) and the 3 tanks cloeser to 5PM.
Cove's in Nassau has a 45-60 min. van shuttle from most properties since they're on the south side of the island and most things are north. Bahama Divers is a better option as they're across the bridge from Paradise Island and 10mins from downtown/Cable Beach. For the wife there's a shuttle that runs around Cable Beach./downtown and another to Atlantis. Also a fery over to Paradise Island from near the cruise dock.
Maybe Grand Bahama? Several shops are based in the marina area and two of them do Tiger Beach from there on all day trips. Unexso does the shark/dolphin dives and I'm a fan of Fred Riger at Grand Bahama Suba - he dives the Theo among other interesting sites.Pretty sharky there also.
One of the shops is based at the Wyndham - they go to Tiger Beach. I believe Unexso also has a small affiliated resort and Bell Channel Inn also has a dive operation. Grand Bahama is located at one of the south resorts also afaik.
For the wife, the beaches are nice, there's a touristy market area downtown and a casino. The marina area is also pretty nice. I've heard Freeport itself has declined but most of the resorts are elsewhere..
I would guess Bahamasair is direct from Orlando?
Good points, I think that focusing on direct flights would also exclude Bimini because I don't think that you can fly direct from Orlando to Bimini - is that correct? And the direct flight criteria might also exclude Cozumel. You can probably get to Provo from Orlando pretty easily but I still have concerns about the possible lengths of the boat rides to the reef.
OP, we are narrowing it down for you! It looks like your best choices for a short trip in early January may be Jupiter FL, Grand Cayman, or Grand Bahama, and possibly Nassau and you are most likely to see sharks in Florida and Grand Bahama or Nassau. You may have the best chance for warmer, calmer water in Grand Cayman but no guarantees and fewer sharks.