Playa Del Carmen is amazing, MUCH better than Cancun. Cancun is basically just a mini America with all the establishments and comforts of home. Playa del Carmen has more of an identity, more bohemian. Everyone is super friendly.
First things first since this is your first time to Mexico: don't be scared. Don't be scared of the cartel, or drug wars, etc. All the things you most likely hear, happen thousands of miles away. It would be like saying you don't want to go to New York because of drug wars happening in Texas.
In Playa you should see Fifth Ave, which is a street with no cars allowed - it's 100% walking. There's shops, restaurants, and hotels. This is the place to be for nightlife as it's sort of like a power line that feeds the city at night. There's clubs, there's lounges, there's live music, pick your poison... However during the daytime, I'd recommend going off the beaten path. Go to the places where there's no tourists (basically off Fifth Ave), discover a part of Playa most people don't. Go to Jaurez street, go south, go west. Might get dodgy in that area at night, but hey where's your sense of adventure? On Fifth Ave you're gonna pay high for food, off Fifth Ave it's ridiculously cheap. My travel style is going off the beaten path, so perhaps you're different and would prefer something different, just throwing it out there.
The beaches are the main attraction during the day, not sure how comfortable you are with public nudity, but Playa is very European and the ladies go topless. Basically, the further north you go up Mamitas Beach, the more nudity you'll see.
Cozumel is good for a day trip, rent a scooter and you can make it around the island in a couple of hours with taking stops. Go snorkeling, there's no snorkeling in Playa.
Check out Tulum, that's where all the Mayan Ruins are. Truly an amazing sight.
Check out Xel Ha, a natural lagoon. Has a lazy river and other neat stuff. You can swim with dolphins too. Admittedly, it is very "touristy" with a lot of obnoxious travellers, but it is pretty neat. Hey for a little money you get unlimited food and drinks.....let's party!
I haven't been to Isle Mujeres, but I've heard great things about it. Apparently has the best beach in the world, but again has a lot of tourists.
In the end, just have fun. Explore, get lost, find your own way, drink like a fish, meet fellow travellers.....you'll have a blast.