There isn't a lot of great snorkeling near the city. However you could catch a plane to either Ambergris Caye or Caye Caulker and do a scheduled tour.

Here in San Pedro (AC) snorkel tours head out around 2pm and take a couple of hours. You could catch the 5pm plane and be back in the city around 5:30pm

Or, alternately you have time to go to Cucumber Beach right outside the city and check out the "Old Belize" museum.

Have a great visit.