Couple of things to add.
If you go to see the Cathedral (it's beautiful inside), do not fail to notice the "Star of David" incorporated into 28 stained glass windows. Legend has it that when the Catholics were building the Cathedral, they were quickly running out of money. A wealthy local Jewish family stepped in and provided the funds to finish the Cathedral. The 28 Star of David symbols was a way of thanking their wealthy benefactors.
Walk a block further and go into the Pino Suarez Mazatlan Market. If memory serves, when you first walk in to market, it's all Mexican trinkets, etc. - but keep walking deeper into the market for a real eye opener (or perhaps gaze averter). It's a big building (occupies a full city block) but totally worth it to see it all. This is not Walmart shopping but a traditional Mexican market. Do not miss.
Next up is the Plazuela Machado (at the corner of Constitucion and Carnaval). Pretty neat area with a lot of outdoor restaurants. Not a bad choice for lunch or a snack.
Then head down Carnaval to the Teatro Ángela Peralta (aka Angela Peralta Theater). I believe they offer a tour but I haven't done it so can't really comment. My experience was limited to peeking in thru the windows. Looks beautiful.
Finally comes my DO NOT MISS suggestion. A block further down Carnaval is the Nidart Gallery (free). Just a fascinating place to see. Wait till you see the Masks and other art. This is some truly special stuff. LIMITED HOURS, generally 9am-2pm so plan accordingly. Be the ones on your cruise that can tell everyone else what they missed. Take some pictures - and then be able to show them What They Missed.
https://goo.gl/maps/JwxcEcJJyZcrQYGF6
I'll throw in one last off topic suggestion. Puerto Vallarta also has a pretty amazing church as well. Down at the far end of the Malecon (my opinion) is the Parroquia de Nuestra Señora de Guadalupe. It's beautiful inside and completely different from the Cathedral in Mazatlan. The interior is done completely in white offset by beautiful gold leaf accents. Definitely worth seeing.
https://goo.gl/maps/bUcK18XjVNAmVDwaA
A little further down the Malecon is the Isla Río Cuale (riverwalk). A beautiful oasis with shopping and food. Trinket pricing tends to be just a little higher than in town (probably due to the location and perhaps higher store rents). But if you see something you like, then buy it. Or perhaps spend endless hours wandering around looking for the same thing at a better price. You're on vacation. I made the "mistake" of telling my wife that if you see something and you really like it - then buy it. She really took that to heart. Subsequent vacations, she buys every thing she likes - whether in Sedona, AZ, Grand Canyon, AZ, Yosemite, CA, Solvang, CA, Alaska or anywhere else. But "happy wife ..."
Further down the Malecon is just a sea of "toes in the sand" beach bars and restaurants - but what ever floats your boat.