Mazatlan meets many of your requests. The beaches are not just good... they are fabulous! From the calm and shallow waters at Stone Island to the surfing areas at Olas Altas and Cerritos/Bruja to the miles of beach along the Malecon and in the Golden Zone -- no problems finding beautiful beaches in Mazatlan! While we did not snorkel on our vacation last December, I understand there are areas at Deer Island and Stone Island where a person can snorkel -- but I don't think snorkeling is Mazatlan's claim to fame.
We stayed in Old Town (Centro; Historical Center) and absolutely loved it. Mazatlan may be a big city, but Old Town does not feel that way. It does have that charming "Old World" feel to it. It continues to undergo a renaissance and many of the old buildings have been restored. My favorite part of our trip was walking through Centro (day and night) and admiring the architecture. There are also an abundance of boutiques, museums, the Plaza (Plazuela Machado), the Cathedral Plaza, the Market (huge, open-air, covers a whole city block), and an array of wonderful restaurants (yes, they call Mazatlan the shrimp capital of the world!). Grocery stores, pharmacies, post office, flower market, fish market, Panama bakery all available in Centro. Dining al fresco, walking along the Malecon at sunset, visiting with the local people -- we were charmed! Wherever you stay, make sure you spend at least one evening dining and people-watching at Plazuela Machado!
No need to rent a car -- and I don't think anyone would advise you to! Taxi cabs, pulmonias, and the city bus are inexpensive and readily available. We traveled back-and-forth from Centro to the Golden Zone. We usually took a pulmonia at a cost of US $3-$5 total. Make sure you confirm the cost with the driver before you get in the vehicle. I understand a taxi is a little less expensive and the bus is only about US 80 cents per person. We could never remember the exact "home" address to tell the pulmonia drivers, so we just always said Hotel Freeman -- they all seem to know that landmark.
The Golden Zone is the tourist center and also has a plethora of shops and great restaurants -- as well as beaches that go on forever! I'm sure you can find quieter accomodations just a few blocks in from the hotels while still maintaining access to the GZ beaches.
My vacation was with my family (12 of us), so we stayed in two beautiful homes in Centro that could accomodate all of us. While I was doing my research, here are some smaller (single-room rental) lodging options that I found good feedback on:
Golden Zone - Captain Moe's Bed and Breakfast
Centro (Old Town) - Hotel la Siesta; Best Western Posada Freeman
If you scroll down the sidebar of this site (tripadvisor), you can click on different lodging options and read the feedback others have left. We stayed right next door to the Freeman Hotel and just down the street from la Siesta. Both have views of Olas Altas Bay and are within walking distance of the main historic areas of Centro. There is a bank right next to (or very near) Hotel Freeman where we exchanged our money and used the ATM.
Here are a couple web sites I found helpful when we began planning our trip:
Hope this helps!