There are numerous posts on this forum...usually at least one a week about "Where to stay" and "Who to dive with." A search, or simply scroll through the posts will bring at least a weeks worth of reading.
Where to stay depends on what you like... We don't like the all inclusive resorts on the South end of the island. We stay in town at Casa Mexicana. Nice rooms, included fantastic breakfast buffet, $70 a night ish, and within walking distance of almost everything we enjoy. La Perlita take a cab, but we walk most everything else.
Who to dive with? again, what do you like? We dive with Aldora because they pick us up at their dock about a half a block away from the hotel and they use steel 120 tanks for longer dive times. They also have at least 6 boats so you are grouped with divers of the same skill level. If you are diving with new divers, that wont matter as much.
Christi with Blu XTsea and Dave with Aldora are huge supporters of this site. Both run top notch operations. We have dove with Dive with Martin and Blue Magic and have nothing but good things to say about them. Tres Pelicanos has a large following on this site too.. Primary differences will be cost, tank size/type, pick up point, pick up time, # of boats, surface interval location, snacks on the boat, # of divers per boat, surface strategy (as a group, timed, or as you hit 700 psi) and several other minor differences as well.
You really cant go wrong on Cozumel as long as you stay with an op using smaller boats with no more than 8 divers. There are some cattle boats operating so I would stay away from those. If you are diving with a group of at least 4, you might consider chartering your own boat through any of the operators listed in this post. We did that with DWM on our first dive trip with our daughters and it worked out great. I believe the going rate is $400 ish plus tips.
Its not hard to find great dive operators in coz, its hard to find the operator that works best for you. Luckily, that just means trial and error (not really error...), several trips, and meeting lots of great people and making new friends.
I also saw your question about crime on the lionfish post. there is a similar post last week. We have walked everywhere in Cozumel and never felt overly concerned. I'm naturally wired a little paranoid anyway but have not had a situation that I was apprehensive about. I still would not get in a beat up van with a sign that said "Free puppies, candy, ice cream, and beer" on the side of it....ok...maybe depending on what kind of beer. I would say that the crime rate per capita is much lower than the main land. Probably much lower than Jamiaca, Honduras, or the DR. Keep your senses about you, don't do anything overtly stupid, (pass out on the sidewalk with your purse next to you) and stay with someone when walking and you will be fine. Like anywhere else, don't look like an easy victim. Assholes are everywhere, but our experience in Cozumel is that by and large the people are very warm and friendly. I have too many stories to support that to include here. We like it so much we plan to move there for the better part of the year within 10 years.
Good luck, safe travels,
Jay
