Of your choices, my picks would be Cayman or Turks/Caicos for your wife. The diving is not too shabby eiher...
Probably Cayman. Seven Mile Beach is actually about 5 miles long. It's a nice beach Stay anywhere along it and close to a dozen dive shops will pick you up for boat diving - 2 tanks and you're back b4 noon. Lots of good deep wall diving, the Kittiwake is a rec cleaned wreck and in case you could talk her into snorkeling, she could do it above you off he same boat. Also Stingray City is the best 15' dive in the Carib. Really the shpp pickup makes it ideal for a couple sharing a car, she can have it while you're gone.
Caymana is an area all about shopping - so is downtown Georgetown except there's a lot of cruise traffic there daily as the port is downtown also.
There's a lot of nice restaurants, some world class, many watefront. There's the Queens Botanical Gardens, kayaking, stand up paddleboarding, several of boat tours - even a real sub in case she's interested in where you dive - it often shows up around Sunset House to view the divers - they know the schedule if you want to wave at her. Anything you can do on the water, beach horseback riding, jetski's, there's the Turtle Farm, Rum Cake factory, some other touristy things.
There's virtually no bugs, the island is extremely clean and I don't believe they allow crime.
Downsides - its' really pricey - everything is imported. Also your timeframe is the start of hurricane season and they occasionally catch one.
Turkls/Caicos - specifically Providenciales (Provo) is smaller but equally nice. Grace Bay Beach is so nice it has it's own website. There's some other water related things like boat tours but much less than on Cayman. World class shopping at sevreal malls - at the Salt Mills the Gucci store is next to the Rolex store etc. Lots of money there also. I think there's two casinos for something to do one night - I've been to one of them. If it's of interest, the Ports of Call is a former Comfort Suites - not beach front but several blocks away. The draw for your wife might be the attached shopping mall..
Diving is about 100% boat diving - they pick up in the tourist areas. There's some diving off Grace Bay - too far to swim - and the NW Point area of the island. But the best, sharkiest diving is off West Caicos or French Cay - about 45-60 mins by boat plus another 15 for the shuttle ride. 2 dives and you're back around 2pm, add a 3rd and it's closer to 4:30. They do lunch on the boat. It's also excellent deep wall diving and at the more remote locations the fishlife seemed oblivious to divrs - I followed some sharks around filming while they did what sharks do. Lots of rays also.
Nassau could work better for her than you. Cable Beach is a nice, but sometimes crowded beach. But there's others - we went to one once where we and another couple were the only one there for hours.
There's a lot of shopping, a tourist market in downtown near the cruise port, some nice shops in the area, the Atlantis mega-resort on Paradise Island has everything, shops, casino, beach, dolphin encounter, etc. There's also several trolleys that run around downtown, to the shops, Cable Beach and over to Paradise Island. You can also take a ferry across the harbor from Atlantis to downtown Nassau.
For you there's 2 dive options (surprisingly that's all) Stuart Cove's on the south side, they'll pick you up in town, at Atlantis or Cable Beach properties. It's a 45 min ride to their location or more depending on stops. They offer the famous shark feed dive in the afternoons and there's several wrecks they dvie - a couple are old James Bond movie sets. Even Cove's buildings were used as a movie set for Flipper. They also do all the cruise dives.
Bahama Divers is across the bridge from Paradise Island. They pickup there and at Cable Beach but not downtown so they miss most of the cruise traffic. One of their signature dives is the Lost Blue Hole but it was better when the hammerheads still lived there. Bahamas diving in general is pretty sharky - we saw reefies all the time.
Nassau is expensive in odd ways - like the airport taxi ride - IDK why. So if you're not getting a car see if your resort offers pickup. Also food is really high there.
Both Turks and Nassau also catch hurricanes so I might buy travel insurance during your timeframes. That's one thing attractive about Aruba - the ABC Islands are below the hurricane belt.
hth,
