Great to hear that you are coming to the island!
There are now three operators on the East End. As Steve said Red Sail out of Rum Point (certain days) and Morritts (every day), Ocean Frontiers from Compass Point and a new one at Reef Resort - Silver Sands. OF and RSS are both good operators - que the normal comments about who prefers which one - I have dived with both. Have not gone out with Silver Sands as yet so cannot give any review on this one. Some of my favourite site are on the south east corner, this is well worth the money for a boat trip if you have the time.
Shore diving: if you are looking for managed sites then these are all on the West Side - Sunset House, Don Fosters (part of the reef is being restored after a cruise ship anchor was dropped in the wrong place. Cayman Magic Reef Recovery on facebook if you have a spare morning and want to help out), Eden Rock (yawn, if there are no Silver Sides there), Sundivers at Macabuca Bar - I like this one, Light House Point - like this one also, and Cobalt Coast.
Un-managed sites: lots and lots, especially along the south side of the island. Just keep an eye on the weather and make sure you have the DSMB handy and bring booties as alot of entries along the south coast can be over Iron Shore.
Winds: throw a stick in the air. Prevailing winds are from ENE, but this can and does change; you can check windguru and passage weather for reasonable 7 day forecasts. If you do decide to stay on the North Side of the island, rent a jeep, throw your gear in the back and look for the dive moorings, this way it doesn't matter too much what the wind does. As normal, tell people where you are going, what time you expect to be back, make sure your gear is set up right, stay safe, if you are not sure about it - pick somewhere else.
Gotta agreed with previous, i would not recommend swimming out to the Kittiwake. Book a dive boat. A lot of operators go there Epic, Living the Dream, Indigo, Dive Tech and others go out from West Bay Dock. Seasports, DNS? will pick up form Seven Mile Beach. Red Sail (and others...although I cant remember the names right now) will do snorkeling only trips out there as well as diving.
Enjoy your time