Turtle Reef is another easy shore dive just north of Seven Mile Beach. Easy entry through a protected cove and about 40-45' to the bottom of the mini-wall. We spent two whole dives there, there's lots to see. IMO, it's the best publicly known shore dive on GC.
Sunset House in south Georgetown is worth an afternoon also. Another easy entry through their salt water "pool" and signature dives under 60' - the LCM Nicholson and the Amphitrite Mermaid statue. Also check out the Cathy Church photo school/gallery on-site. My Bar there is a diver's spot.
Stingray City is the most fun you'll have in 14'. The dive, not the nearby snorkel. Most diveops will do it as an afternoon dive.
Besides Neptune's Divers, other small group-size operators often mentioned here are Wall to Wall, Off the Wall or Ambassador Divers. All (should) pick you up at the Westin.[user]Caymancase[/user] here is Casey from Neptune's. Since they only take 6-8 divers, you'll be 1/2 their business.
Red Sail is the on-site dive operator at the Westin.
Red Sail - Westin Casuarina Resort and Spa. Fosters is downtown so when the cruiser's are in port daily, that's an issue. Neither would be my choice but I don't like diving with big groups/
boats - ymmv.
If you dive Eden Rock, they're about 100 yds. north of the cruise terminal so plan that for late afternoon or a non-cruise ship day. People who've not been there recently probably haven't experienced how 2-3 cruise ships in port change Georgetown now.
Google it, there's an on-line cruise schedule for Georgetown. We went thru there on a 2-ship afternoon - note that people often don't look your way as driving is on the opposite side - b4 stepping off the curb. By 5-6 things quiet down nicely if you want to explore some of the restaurant/shopping options downtown - some of the shops close when the last boat leaves.
One thing to mention when booking, typically the first dive on most 2-tanks is deep down the wall - 100' +/-. Some dives have a shallower option, others start around 60'. So mention your dauqhter's dive experience. Aquarium is a really good shallow dive at about 45'.
More info can be found in the Cayman Islands forum. I've moved this thread there now.