We had a nice tour of Old Mazatlan via a tour bus scheduled through our hotel. The driver was very accommodating, speaking every description both in Spanish and English so everyone could understand. We stopped a few places along the way, and the driver explained various things about the city. Old Mazatlan has very narrow streets and some lovely old buildings. There were also some very interesting artisan shops. One thing that was a little disturbing was the amount of bars on windows and doors, and things falling into quite a bit of disrepair.
You could also take the bus into Old Mazatlan and walk around on your own, but it is suggested that tourists do this only in the daytime.
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