I thank you for your questions. I am glad that you have enjoyed mazatlan. There are several beaches to go to. Many people enjoy the beaches of stone island but it is more for relaxing, not much shopping except for the vendors.
If you like to do both, beach and shopping, I would say go around the beach where the Hotel Playa is or Hotel El Cid. Those hotels are in the golden zone so once you finish doing the beach you can always go shopping. There are plenty of taxis to take you back to the ship. Now, if you want to buy things that are not touristy, like, sandals, dresses, shoes, etc, then the best place is downtown or the shopping mall called La Gran Plaza.
So think of what you want to do and then decide from these places.
If there is anything else you want to know or something is not clear, please ask again. It will be a pleasure to answer.