Steve Gerrard is a highly experience cave diving instructor, a very fun and patient guy.
http://www.deephorizon.info/index.phpHe is the author of the book Cenotes of the Riviera Maya.
http://www.cenotesoftherivieramaya.com/I do not know if he would be willing to take you on caverns dives, but if he won't Steve will be able to recommend a good, ethical, reliable dive op who can. You've got to be careful, some dive ops will exceed the maximum number of clients per guide in order to make more money. This puts you at risk. If you see your guide doing this, call it to their attention and make them get the proper number of guides.
Just a reminder, the cenotes are very fragile and precise buoyancy control is required so that you're not stirring up the bottom (and reducing visibility) and so you don't have to be grabbing onto formations.
As far as the Mayan ruins are concerned, Tulum and Coba are nearby. If you plan to return to the Riviera Maya, I would start with Tulum. It's incredibly beautiful and easy to get there. You can visit Coba on your next trip. You can do both Tulum and Coba in one long, long day.
You can take a bus to Tulum and catch a taxi out to the ruins, or drive there. If you're really slow it will take about 1/2 a day to see everything. Take some beach clothes and hang out on the beach at the ruins. There are many good places to eat lunch/dinner in Tulum.
Coba is a bit off the beaten track, about 45 minutes west of Tulum. You'll need an entire day and good walking shoes. Everything at Coba is spread out and it's a long walk to go anywhere. There are a million people with bicycles who will give you a ride for a small fee if you don't want to walk. Take insect repellent and lots of bottled water no matter where you go.
There is a pyramid you can climb at Coba, really cool experience. Due to the way it faces, you'll get the best photographs from the summit of the pyramid if you can get to the top before 11:00 a.m. The best view to to the south/west, and later in the day you'll be taking photos looking directly into the sun. Views to the other directions are blocked by trees. This necessitates an early start to your day, and once at Coba make a bee-line to the pyramid. After you've been to the top of the pyramid you can see the rest of the ruins at your leisure.
Chichen Itsa is too far away for a day trip, in my opinion. You can fly there from Cancun airport and back in a single day, but that's too much work for my taste.
Obey the speed limit, stay low key, and you'll avoid getting stopped by police. They're all on the take. Keep very little cash in your wallet, so when it comes time to bribe the police you don't have a wallet full of cash. I've been stopped once in 5 years, had to pay $100 bribe to keep from getting jailed for "speeding."