In the Bahamas we have stayed and dived New Providence (Nassau) and Exuma. The diving around New Providence was IMO not that great though we did get to see quite a few sharks. The diving in Exuma was better - blue holes, smaller intact wrecks. Comparatively the diving I've done in the Bahamas was not as good as anywhere else I've been. In fact it's last. Bear in mind I have not dived everywhere in the Caribbean.
There is not alot topside in Exuma to do for non-divers. There is snorkeling, the swimming pigs, golf course, some tours and the beaches were exceptional. Alot less people but harder to get to. We stayed at Sandals in Exuma but mostly used an off site dive op which I recommend if you want more diverse sites and bottom time. As of a couple of years ago there is only one dive shop and they are expensive. Taxi fares are outrageously expensive. Think about renting a vehicle. I have trip report on SB for this trip. There are other hotels on the island but again, less people and tourism in Exuma.
Nassau will offer much more to do for a non-diver. Nassau is loaded with hotels from budget to expensive so I will leave that to you. We stayed on Cable beach which is a nice beach. Overall I probably would not return to Nassau for at least diving. It has the typical cruise ship shops and a straw market which we did but I just hated it. We were mostly treated like sheep to be sheared. It's not my thing. Nassau as I recall has quite a few historical landmarks.