Nothing around the airport - literally. Just a few industrial buildings and land to build a bigger one if they ever do. And it's a small, old, crowded airport.
They'll want you off the ship by 9AM Saturday so they can prep for arriving guests so their shuttle driver will take everyone to the airport or other destinations. Which will most likely be too early for your flight back - at least it was for us on USAirways thru Charlotte. Our whole group camped out in the small restaurant - at least there's WiFi. The USAirways agent didn't even show up till after 11AM so we left luggage where we could see it thru the window.
Once you see the line starting to form for security screening - get in it. I'm not sure why but the line seemed to go from no one to about 200 people in minutes. if it's still the same there's only two checkpoints and one scanner. On the other side you'll be in a big departure lounge that serves 4 gates clustered basically next to each other. There seemed to be a window from about 12:30 - 3:30 when they tried to get everyone out as quickly as possible - organized chaos. One of the crew was flying home with us, he said it's always like that.
Since you're not beach people, the fact that Grace Bay Beach is one of the nicest in the world is ironic.
I had a pretty good time in that area although we were only there from Saturday about noon till sailing and Friday afternoon/dinner afterwards. There's both upscale and casual restaurants in the area, shopping at the Salt Mills and most of the other touristy things associated with a Caribbean paradise - it really is stunningly beautiful there. There's also a small casino or two - they have a free shuttle - your hotel can call it for you. And it was free except for tip - both directions. They even took me back to the Explorer late Friday night which is a good 15-20minute ride south. Other options:
Turks and Caicos Turks and Caicos Tourist Board - Providenciales - Activities
We ate as a group Friday night at Danny Buoy's - even bought the crew dinner. It's one of the places they'll suggest - nice outdoor dining but not overly fancy or pricey. It's a bar with a band later at night also.
Danny Buoy's: Beer - Food - Sports - Music | Serving Providenciales, Turks and Caicos Islands
Somewhere affordable in the middle of things is
Ports of Call Resort | Turks and Caicos - it used to be a Comfort Suites. It's in one of the smaller shopping complexes and Salt Mills is nearby. A lot of the amenities are clustered in that area also. Anything on the beach is more expensive. Decadently expensive is Amanyara but IDK if they do single nights...
That trip is probably the best liveaboard we've done in the Caribbean. You get tired of seeing all the rays around the moorings and sharks at French Cay is almost guaranteed. Turtles all over also. Some huge lionfish down the walls also. We heard but didn't see the dolphins at West Caicos also. I always seemed to find Cuda also and I was able to get close on several occasions. You can see the symbiosis between the Stingray's and their companion fish (Grunts?) at many locations also. Not a lot of divers get out there so you can get really close. Night dives are cool too, the Conch come out and you can follow their trails to find them. A big old turtle ambushed me at West Caicos - the DM said he does that often. Charged me then veered off at the last second just off the mooring.
I link to it all the time here but if you've not seen this - Mike Southard wrote a good review a few years back -
Saudio's Trip Reports
Have a good trip...you will.