When you say "charter" do you mean you're paying the $1500 or so for a private charter just for the two of you? If so they'll go anywhere you want and East End Divers suggestion would be a good one - Babylon is among the best. For that kind of money, Indigo Divers would be my choice also - they'd likely pick you up at the port in the Escalade as well.
Or are you using "charter" to mean you'll be paying your $100+ for two dives on someone's boat along with other divers? If so:
Being new divers it's much less likely someone will take you to the North Wall, it's deep, there's currents and it's too far from Georgetown. After September the likelihood of it getting blown out due to weather increases. Even some of the more exposed shore dives in that area are "difficult" at that time.
A typical dive profile is going to be up to 100' on the first dive and 40-60'ish on the 2nd. As new divers 100' is not a very good idea even with a DM since you'll burn thru your gas a lot faster and have to surface sooner. Since it's your only dives, I expect you'd like to make them last. So I suggest you disregard the North Wall suggestion.
Generally most of the year the West is the calmer side of Cayman so that's where less experienced divers are taken. There's a lot of good shallower sites there as well. Unfortunately I don't know many of them as we dove deeper mostly.
Decent sites within your range might be:
The upper decks of the Kittiwake if you like the idea of diving a wreck. It's been prepared for divers so is as safe as possible. They cut big holes in it so you can almost always see an exit point. It's sitting on the bottom at around 60-70' and the top nearly breaks the surface. There's two options - one is diving down the outside of the wreck, the other is penetration of the first 3 levels. A DM is required as an escort there - actually everywhere on Cayman. Your DM will take you in and out at your level if you decide to try the penetration.
The Official Website for the Kittiwake Shipwreck - Home
Aquarium nearby is a decent shallow dive (40-50') with lots of coral heads on a sand base. So if your buoyancy isn't optimal (it won't be if that's your first warm water/ocean dive) you have a place to put a fin down without damaging the reef/coral. Also it's interesting, look for aggregations of fish hovering in one spot above a coral head. Often as you get closer you'll notice fluorescent red and blue cleaner shrimp at work. Hold out your hand to one slowly and they'll "clean" your cuticles. They have really
sharp but very small claws.
We also dropped on Governor's Reef once. I'd suggest they pick a different site if offered that one.
Wall to Wall (and others) also will dive south from Georgetown. The Japanese Gardens sites (there's at least two) are shallow and interesting with some swim-thru's and other fun stuff.
Dive Sites | WalltoWallDiving.com ? Personally Guided Grand Cayman Diving at it's Best!
Another option might be a couple of dives in the morning and Stingray City in the afternoon - if you have a late enough sailing. It really is the most fun you can have diving in 15' of water. It's the other "signature" Cayman dive experience.
Typically most of the operators go out there around 1PM, it's about a 20min. drive from the port to the marina where they keep the boats, it's a 10? min. ride out, a 45min. dive. So about 3 hrs. total Whoever you choose for your morning dives likely offers the SRC trip also. We did two morning boat dives (shore based) had lunch and did SRC that afternoon - back by about 4:30 and our condo was 10mins from the port. That's also likely offered by your cruise line, both a dive and a snorkel at the Sand Bar nearby.
If it's of interest, Don Fosters is the cruise operator. They're about 100+ yards from the cruise tender port and even offer a shuttle. Although that might be a good option for newer divers, you seem to indicate that you expect to have some input into where you dive. So will the other 18-24 people
possibly on the boat. It doesn't affect safety since they'll provide a DM for every 8 divers but why do that when the smaller operators only go with 6-8 divers max. It's been my experience that the more divers, the more the fish run and hide.
I'd focus more on choosing a recommended operator from input here and elsewhere. Also if you choose someone based up on Seven Mile Beach, you'll need to make arrangements to get there yourselves most likely. Boats leave around 9AM typically. If there's a lot of cruise ships in the harbor (I've seen 5) tendering in can take slightly more time also - there's no cruise pier on Grand Cayman.
There really are no bad operators on Cayman. They all charge the same and provide basically the same level of valet service so the bad ones don't last long. Be clear about your level of experience no matter who you book with so they can provide the best possible options.
