Cozumel is the name of the island. The one and only town there is called Cozumel, and YES it's quite safe to walk. U just take normal precautions, u'd take anywhere.
We've done various things there. Probably the most fun we had was doing the Jeep Safari in the morning, and then walking around town in the afternoon. And U HAVE to go to Carlos & Charlies!!
Its also easy to rent a jeep on your own in Coz. and tour the island. Its small, only one main road around it, and u can stop at various beaches, to relax, snorkel or whatever.
If you are not comfortable driving, a taxi to the ecological park with underwater snorkeling trail is highly recommended; Chankannab (sic) or just take the taxi to Plays del Sol. A good ship's tour if you are interested in history is to Playa del Carmen and Tulum. Well worth the fee. If your cruise included Grand Cayman, be sure to take a Swim with the Sting Rays tour either on your own or a ship's tour. Dunn's River falls climb is highly recommended in Ochio Rios.
The Main Street in Cozumel is lined with shops and cafe's for the tourist trade. Be sure to stop into Poncho's Backyard which is inside Los Cincos del Sol at the end of the main street. The store has every kind of souvenir you could want and the restaurant is located in the back including strolling Marachi's.
Cozumel is my most favorite island and just a wonderful place to be. Crime towards tourists is as close to being unknown as anyplace I have ever been. I have never had one minutes worry about walking around anyplace there including the town of San Miguiel. Lots to do and see there from snorkeling and diving, to sightseeing, 4x4 safari's, horseback-riding, and shopping and of course the wonderful and wild Carlos & Charlies. Have a good time and toast one for me.