We took a tour through the cruise line to see Tulum. The ship docked in Play Del Carmen to let the tour passengers off, then went on to Cozumel. They tendered us back to the ship after Tulum. This took 1/2 a day, and we spent the rest of the day in Chakanaab Park. I highly recommend this. Great snorkeling, covered lounge chairs, very pretty beach. I cost $10 to get in. We took a taxi there. I forget how much the taxi cost, but it was minimal.
I will agree with Kim here. We have done the Tulum tour from the ship and as a history buff I loved it! They will also stop halfway there for a "necessary break" but it just happens to be at a souviner place. <G> The ride back they served beer or soda onboard the bus. There is time to go to the lagoon and swim and even time after that to go to town and do some shopping and stop by Carlos and Charlies for a nightcap. Just don't get too nightcapped and miss the ship! <>
I totally agree with Robo and Kim. Take the ship's tour to Tulum. They will only let you off in or for tendering to Tulum if you have bought the tour. Save your souvenir shopping for the craft booths at the historic site. You can barter with the vendors. Once you tender back to San Miguel, you can shop, go to the beach; Playa del Sol is a $12 taxi ride each way or Chankaanab Park as mentioned. The ruins at San Miguel are not as vast and exceptional compared to Tulum and Chitzen Itcha is much too far of a trip unless you fly $$$.
If you don't mind a long day, the tour to Tulum is quite fascinating. I definitely do concur with the recommendation to stick with the ship's tour due to the time and logistics involved. If the tour runs late, the ship will wait for it or, if it misses the ferry connection, make the necessary arrangements to get the passengers back aboard. If you go on your own and run late, you are on your own (and please excuse the pun).
If you go to Tulum, be sure to take a large (liter) bottle of water from the ship for each person in your party and be sure to drink from it frequently, especially while visiting the ruins, to prevent dehydration. The climate there is very warm, with normal daytime temperatures in the 90's even in the middle of winter.
If you prefer a less ambitious excursion, there are some Mayan ruins at San Gervasio on the island of Cozumel. The ruins there are less extensive than the ruins at Tulum, but they are more significant because the island of Cozumel is sacred in the Mayan religion.
There's also a relatively new archeo-ecological park at Ex Caret, also on the mainland, that supposedly has some excavated ruins in addition to a lagoon for swimming and snorkeling. I don't know too much about it, but I again recommend taking the excursion from the ship rather than going on your own due to the logistics involved.
Chitzen Itcha is a long way from Cozumel and Playa del Carmen. Some cruise lines do offer excursions there that do indeed go by air -- and they are very pricy.