My opinion...if you only have a week plus a day or two, island hopping will end up taking a couple of days out of your dive schedule as you shouldn't dive 24 hours before flying and you probably won't get a dive in the day you arrive at your new destination. I always like to do multiple days of diving at any particular destination...not every dive is that perfect dive which will represent the whole country.
Turks and Caicos is my personal specialty. Night dives are not very common in Provo. First, you don't go to where the best diving is as the boat ride is too far. If you go, the dive op will take you to the reef in front of Grace Bay. We did one out there last summer and it wasn't very good. Much of this had to due with the fact that it was still light out at the start of the dive. So, I'd make sure to ask your dive op what time they go out to make sure that it is at least dusk when you hit the water.
Back a few years ago, we went to the dive shop over at Coral Gardens and the divemaster took us on a shallow shore night dive around the snorkelling reef. It was pretty good and he took just the 2 of us. We've tried night snorkelling too...always some interesting critters to see, even just in the sand.
All of this being said, if you like big animal encounters, we've seen some great big animal life in Turks and Caicos during the summer, including reef sharks on almost every dive (they like to come pretty close sometimes too), nurse sharks, dolphins, eagle rays, and even a hammerhead shark once off in the distance. Also, there are turtles and some nice fish life too. The water is so warm, I don't need to use a wetsuit anymore when diving in the summer.
Grand Turk would be another option. They do more night dives over there because the dive sites are so close to the shore. Personally, I prefer the diving in general at the spots accessible via Provo like West Caicos and French Cay, but Grand Turks is very nice too. What I don't like about Grand Turk is the cruise ship traffic. We really enjoyed our stay at Bohio Dive Resort until the beach was suddenly jam-packed with cruise ship passengers. Luckily it was only once while we were there. Would not have been happy if that happened every day!
We've travelled to Turks and Caicos in July or August for the past few years. We've never had bad weather in July, but were there during Hurricane Irene in mid-August back a couple of years ago.
Have fun planning your trip!