It really depends on what your interests are, what kind of boat you'll be chartering (cat vs. monohull), and whether or not you're permitted (or willing) to traverse the Whale Cay channel to the more northern cays.

Some suggested places to stop include:

Hopetown - nearly landlocked harbor, charming village, beautiful ocean beaches.

Little Harbour - shallow entrance bar, so you need to make sure you have the right tide/keel to cross it. Snug anchorage, Pete's Pub (infamous), Pete's foundry.

Great Guana Cay - depending on weather, several anchorages to consider, giving access to Nipper's (beach bar par excellence), Spoil Bank Cay (shells shells shells).

Tilloo Cay/Tilloo Bank - weather-dependent, but an amazing sand bank and an appealing beach on an almost uninhabited island.

Green Turtle Cay - both Black Sound and White Sound provide all-weather protection and moorings; access to New Plymouth settlement; beautiful beaches; a few marinas; great restaurant at Green Turtle Club.

Manjack Cay - like Green Turtle, north of the Whale, but a cool, nearly uninhabited island to visit with beautiful beaches, semi-tame stingrays, beachcombing.

Treasure Cay - haven't been there myself, but reputedly stunning beach.

Etc. etc. etc.