Playa Norte

This is by far the best beach of the island and one of the best beaches of the world! It’s located in the North end, in downtown.
You will find super calm and shallow waters and bright white sand. You can choose a quiet spot in the sand under a palm tree where you can lay your towel and relax or find a great restaurant with all the services they provide.
The restaurants in North Beach offer showers, food and drinks, toilets, chairs and tables and beach beds. They are more like beach clubs than just restaurants. Some of them charge you an extra fee for the beach beds and then it goes towards your consumption. Some restaurants just charge the fee as an extra apart from your bill.
Some of my favourites are Tuturreque 33, Fenix and Mayan Beach. You can find live music on Sundays! Most of the times they play Cuban salsa, lots of fun!
The sunset at North beach is a must, please make sure you get to see it at least one day

Here is a link to find out the sunrise and sunset time: http://www.sunrise-and-sunset.com/en/sun/mexico/isla-mujeres

Other Beaches on the Island

There are some smaller rocky beaches on the Caribbean side (opposite to the bay side) of the island. I would not recommend to swim here unless it’s a very quiet day with no wind. On windy days this side can get rough and makes it dangerous since there is a lot of sharp coral.
The beaches on the bay side on the way to Punta Sur have not so clear water as you can find more algy. But there are some very good places to spend the day with great food and drinks, umbrellas and beach chairs too. Some of them have a pool so they are also great options. Some of my favourite places are Zama, Capitan Dulche and PLaya Lancheros (Tikin Xic style grilled fish and ceviche are excellent here)