Gary: there are so many good options in the Keys that you almost can't go wrong with any choice you make. I've never dove with Rainbow Reef but there are a lot of SB'ers that really like them, especially since an underwater guide is provided as part of the cost: most dive operators don't provide guides unless you pay an extra fee. I'm not a big fan of guides, but a lot of people enjoy having a local diver point out interesting things to see.
My experience: I tend to use Conch Republic Divers when I'm in the Keys. I've had a lot of good luck with them, they've provided me with some excellent service when I've been in a bind, I like the staff and crew and I like their big boat (wide beam and very very very stable). Sometimes the big boat is full of divers (20+) but that does not happen all that often and I've never felt crowded on it when it is full since it is so big. They also have a smaller boat that provides a little more 'personal' service and usually only has a handful of divers on it. They have an on-line schedule so you can check if they are going to deep or shallow sites. Given Conch Republic is a little further south than most dive operators, they visit shallow sites that few other boats get to, which is kinnda fun.
The other two dive boats I've used are Quiescence and Silent World. Quiescence is a six pack operator (e.g. three smaller boats that hold 6 divers max) and the shop lets you choose the dive site you want to visit. They do offer nice service, but my main dive buddy I go to the Keys with gets sea sick easily so we usually use Conch because of the bigger, wide beam boat.
Silent World ownership changed hands a year ago and I've only been out with them once since. I had a fantastic experience on that trip, but it was on a deep set of dives (S. Grove) and much of the reason I liked the trip is that they did not try to be over-bearing: essentially letting me set my own dive profile and surface interval and letting me dive solo (for which I'm certified and have all the redundant equipment). The captain was a really nice guy too. I don't really know how they operate on shallow dives or with less experienced divers but they give me the vibe that they cater more to experienced and/or tech divers, but I could be wrong about that.
If you are looking for something other than a hotel, I've stayed at this condo a few times and it is pretty nice by Keys standards:
Key Largo Hotels & Resorts | Ocean Pointe Suites at Key Largo | Hotels in Key Largo Florida Keys
I've not stayed here but plan to give it a try this summer when I meet up with a friend from Denver. It seems to be a traditional Key Largo hotel, but cleaner than many (per Trip Advisor)
The Pelican - Vacation Cottages, Key Largo, Florida - 99340 Overseas Highway, Key Largo, FL 33037 - (877) 451-3576
In July, a 3MM should be fine