The Mazatlan Aquarium is a famous destination for Mazatlan travellers.  In 2009 they opened a new Ocean Tank, the biggest in Latin America. The shows are all in Spanish, but are enjoyable even if you do not speak the language.  There are also bird and reptile exhibits in addition to aquatic exhibits. It's definitely worth a visit.

The Market in Old Mazatlan is a great place to experience the culture in Mazatlan.  You can pick up fresh produce or trinkets in the market (be sure to barter).  You may find deals on shoes, purses, t-shirts and jewelry in addition to fruits, breads and vegetables (and meat and fish if you plan to cook).  Pulmonias and taxis will take you there, or the "tourist bus" will drop you off right at the market. 

The Cathedral is right next to the market and is worth visiting.  There are lovely murals and sculptures in the church.  Your hotel will know the times when (Catholic) mass is offered if you wish to attend.  The mass is in Spanish, but there are usually other tourists and many families, so it's not very intimidating to non-spanish speakers. 

Stone Island is a "side trip" worth taking if you have a day to relax on the beach.  Most hotels will give you a better rate than the street vendors who also sell the trip.  The "Adventure Island" company offers a good tour, and will pick you up at your hotel and provide the ferry transportation.  Activities on Stone Island include: Horseback riding, snorkeling (except during jellyfish season), kayaking, and "banana boat" rides.  There are also hair braiders if you want to get that "I'm on vacation" look. 

The malecon along the waterfront is a wonderful place to walk after dinner. It is not shaded in the daytime, so it is not pleasant on a hot afternoon, but it is crowded with families, couples and young people in the evening.  Vendors sell trinkets, teenagers rollerblade, and it is overall a pleasant way to spend an evening.