1 day on a cruise ship means only a certain amount of hours for the day. You don't want to miss snorkeling in San Pedro. Hol Chan and Shark Ray Alley would probably give you a great experience for the amount of time you have.
Papashine has good advice. You can book in advance on your ship or do it yourself. The ship web sites generally have a sampling of the tours they offer. Adhering to the ship schedule is important. It will be hectic but well worth it.
I recommend the street vendors for food - fast and very good - you have to remember you are on Belize time - which means restaurants are not quick. Street vendors are more authentic. The food would be something to experience when you come to stay for more than a day, besides you have plenty of food on the ship
There is not a lot to shop for in San Pedro unless you are into local art, wood carvings, Mayan weavings and hand made jewelry by locals which can be found close to the street vendors in the middle of town. My experience, with cruise ships is that the cruise terminals offer much of what you could find at local shops(caps, t-shirts, shot glasses, etc.) - all in one place and its faster. One item I would not forget to bring back with me is some Marie Sharps hot sauce - the one with the green label is to die for - if you are into that - seeing you are from Texas, you probably are
I hope you have a wonderful trip!