I would echo what MMM says above regarding more information. I would also verbosely suggest the following:
1. If you've never done Cozumel, don't bother with getting to the "advanced sites". There are only a few of them, and though very nice dives for differing reasons, they aren't the hallmark of Cozumel diving. Make sure you get to Palancar anything, (4 different sites) which you undoubtedly will, unless you're there for only one day and you happen to do Santa Rosa Wall as the first dive, or maybe Paso de Cedral Wall. (ya, I know there are other possibilities, but...)
2. If you've been to Cozumel, and done some diving there, of course, and are trying to fill a bucket list or whatever, then I'd do the following: Contact any of the many dive shops that get mentioned here, and tell them exactly what you're after, and honestly answer their questions about skill level, etc. Any shop, any *good* shop, and there are many of them, will want to dive with you for a couple days or so until they take you to the few advanced sites that are dived.
The part about contacting the shop, and telling them what you're after, and giving them honest answers will get you what you're after, assuming your requests or expectations aren't outlandish.
It's really hard though, to make a great, pinpoint recommendation on a dive shop with very little info. We
know that you're going to be in Playa for a month, have some (?) experience and are looking for small boats.
There are a zillion shops in Cozumel that have small boats, and go to the advanced sites. I suspect you've never been to Cozumel before due to the nature of your question, in which case, I'd do Number 1 above and
contact any of the many shops that will get mentioned in this thread, and in others. You'll have a great time!
The diving is famous for a reason.
Here's my cheerleading... The great bulk of my 175 tanks in Cozumel have been with Deep Blue. They fit your bill, as many others will. I know they do the advanced sites, because I've been to them lots of times. They didn't, btw, take me to those sites when I was a new diver. I chose them, almost 6 years ago, because their advertising mentioned sites that they visit which none of the other dive shops mentioned. Not my only, and probably not the best criteria to chose a dive op, but it worked for me. I've had what I believe to be a bunch of really excellent training from them, even long after I completed any courses I've taken.
I've also been diving with Blue Magic and ScubaShack/Roberta's Eco Dive/can't remember. Great shops, Great service, Safe, go to advanced sites, small boats, great DM's and captains. If I didn't dive with Deep Blue, I'd happily dive with them again. Depending on other details of your trip, and that's my point, I might recommend one over the other.
Just to give you an idea, I've only dived with the first 3 shops, but I'd be delighted to dive with any of the following shops if the circumstances permit, and I believe all of them have small boats and would go to the advanced sites. This is based on reading reviews here, and having been to Cozumel 11 or so times. In no particular order... (OK, I do have a little Deep Blue bias.)
Deep Blue
Blue Magic
Scuba Shack
Blue XTC
Aqua Safari
Aldora
Living Underwater
Blue Angel
Dive with Martin
Scuba Mau
Dive with Allison
Blue Bubble
That's just off the top of my head, and does not mean to discount any others that get mentioned. There are
just sooooo many shops that fit your bill. Just make sure you contact them and let them know what you're
after.
Don't know what you're doing in Playa, but if you're into diving and have the time, I'd plan on going to Coz for 5 days. You could get a "5 day - 2 tank/day" package. It gives the shop time to assess your skill for advanced sites. You get a good look at Cozumel diving. Even if you never get to Devil's Throat, Maracaibo, Barracuda, San Jaun, Cantarel (?), or whatever the few advanced sites are, you won't miss them if it's your first trip. Really, I don't think many people would feel like the missed out if they didn't get to those places after their 2nd or 3rd trip. I could dive Palancar Gardens, for instance, for 10 straight dives and have the time of my life.
I think I'd stay downtown. Great food there, no beaches. Maybe Casa Mexicana, on the spendier side. If I wanted to save money, I'd stay at the meager but just fine Hotel Pepita a few blocks off the water. Never been there, but heard good things, and I think it's about $40/night. I've stayed at Casa Mexicana, and it's probably $80-$100/night, right on the water. If you ask for recommendations about a place to stay, you'll really want to get specific about what you want. When I go to Cozumel, I stay at Casa del Mar. I get good a good deal there with airfare, and it's a fit for me, and the people I usually travel with.
It's really hard to have a bad time doing a dive trip to Cozumel. Great diving and dive industry. Great Food. Nice, clean accommodations. Really nice people! It's a great trip. You'll have a blast!!
-Blair