Based on everyone's recommendations for a place in the Cancun area that sounds a little more relaxed and slightly less touristy, we're looking forward to staying in Puerto Morelos at the end of February! Myself and my two kids (10 and 12) will be in town for a week, and are staying in a rental apartment. So far the itinerary includes snorkeling from the beach in Puerto Morelos and a one-day cenote + reef snorkeling trip. The kids are fluent in Spanish, so hoping to do a little exploring. Any suggestions for good day trips, preferably accessible by public transportation? Also curious to know of any kid-friendly cooking classes or cultural programs. Thanks in advance!

This place is right in Puerto Morelos and gets good reviews:
http://www.thelittlemexicancookingschool.com/
You could take the ADO bus from Puerto Morelos to Playa del Carmen and then ferry over to Cozumel.
Coba ruins is a good idea, the kids can climb there.

Does ADO now go into Puerto Morelos? On my last visit, the bus stopped on the highway, about a couple km from the town, requiring a taxi to get into the town. Or a long, hot, uninspiring walk.

No, ADO still stops on the highway, forgot to mention that, so they would need a taxi to the highway which I am told is not very expensive. We always had a car when traveling in the area.

Thanks so much for the tips on getting to Coba! I also found this link about getting from PDC to Coba, and also heard there is a 7am and 7:35am bus from PM to PDC.
So it looks like 3 legs: Taxi from PM town center --> ADO highway stop, then 7:35am bus to PDC, then 9am bus to Coba, getting in at 11am. I think we can do it! Downside: we will be traveling for nearly 4 hours each way, but that will be its own adventure. : )
Another idea is intercity bus or van to Cancun, local bus to Puerto Juarez, and ferry to Isla Mujeres for the day, where you can walk, swim, bicycle or tour the island on electric golf cart.
There are lots of cenotes near Tulum, perhaps some nearer Puerto Morelos, I do not know. If the kids can swim, they will love that.
Also I rented a bicycle a few times in the Yucatan, once near Tulum, and a couple of times near Valladolid. If you pick quieter roads, can be fun and safe.

It would also be fun to take them to Tulum. The ruins are interesting. After we walked around them, we took a boat ride that takes you past the ruins from the water, The boat then takes you out to the reef to snorkel-there weren't quite as many fish as snorkeling off the beach at Puerto Morelos, but the reef was absolutely amazing. If you decide to go, you buy a combination ticket at the gate that admits you to the ruins and includes the boat trip. Have fun-we love PM.

Thank you everyone for your suggestions! Coba sounds great, but the distance and timing (to catch the one bus) was a little daunting. So we ended up taking colectivos to Tulum from PM. If anyone is interested in doing the same thing, here are the steps we took:
After about an hour in the sun walking around the ruins, we walked to the main beach and had a great time body surfing (it was windy, so the beach underneath the ruins was closed). We brought a towel and swimsuits, and then used the outdoor showers near the beach entrance (10 pesos/person) to clean off before heading back to our apartment.