In that case, I have stayed at what is now the "Ports of Call" hotel (when I stayed there, it was a Best Western), and I dove with Dive Provo. (The hotel & the dive shop share a parking lot, so it doesn't get much more convenient.) Dive Provo is a concierge dive service and I had a very good experience with them. Many of the sites require a fairly long boat ride out (45 minutes to an hour), but the diving was great. It is mostly wall diving and the sandy "shallows" are 40 feet deep or more. When I was there, the reefs were full of life and there was the usual big stuff off in the blue and occasionally closer (sharks, rays, turtles, etc.).
After the diving is done, pack up your "boat bag" and leave it on the boat. Overnight they will rinse, dry, and secure your gear and it will be waiting for you on the boat the next morning.
If you wind up going to Grand Turk, I highly recommend a place called "Bohio", but more on that if it looks that you might be heading to Grand Turk.
BTW, the Turk & Caicos Explorer is a lot of fun and great diving too. You really can not go wrong with any of those options.