When staying in Cozumel for a week or so, grocery shopping can be a necessity. Luckily there are two local stores on Melgar that carry almost anything needed for a week in a condo in Cozumel, Chedraui and Mega. Each carry household goods, food, medicine, sunscreen, beach toys and all types of items that travelers might need. Both stores are easy to access from Melgar. Mega even has a parking garage! Pesos and US Dollars are accepted at both stores, as well as credit/debit cards. Don't forget to tip the people who sack the groceries. Most are elderly and depend on tips. The tips are their income!
If you are looking for local vendors, selling FRESH seafood, veggies, meat hanging from hooks and other local items, then the Municipal Market, or Mercado Municipal, is the place to go. It is an open air market located at Calle Adolfo Rosado Salas between Avenida 20 & 25 and is open from 7:00 AM to 1:00 PM. There are many Loncherias, little lunch/snack bars, to try local food. Tacos can be found for about 17 Pesos, or less than $1 USD each. There are usually very few tourists here and many souvenirs can be found here much cheaper than in the tourist parts of town. Bring your Pesos though because that is what most of the vendors accept.
Check it out! It is a fun opportunity to find friendly merchants, great food and lots of Spanish being spoken. You will have a good time and get to see a part of Cozumel that many people miss!