According to the cruise ship tour directors I've interviewed, the most popular tours for passengers are cave tubing (typically at Jaguar Paw), snorkeling at Shark/Ray Alley and the trip to Altun Ha, which on some cruises may be coupled with something else such as a Belize City tour, lunch at Maruba Spa or something else.
You can do these or other tours on your own, but for many people it's best to go with the ship's offerings, for two reasons: First, since the Belize City harbor is too shallow to dock at shore, passengers are tendered in on small boats. With 2000 passengers, this takes a good bit of time and organization, and if you have a tour with the ship you may get priority on tendering. Second, due to the limited number of tour operators in Belize City, and the crush of passengers from the ship, you may not find the tour you want offered independently at a time that will get you back to the ship on schedule. However, if you like to do things on your own you can rent a car (Crystal is at the Tourist Village docks) or take a water taxi to San Pedro or even fly to San Pedro (take a taxi to Municipal airstrip).
For those who don't want to do a tour, the Tourist Village shops are clean and safe and are perhaps worth an hour or so. The new Belize Museum, in the Central Bank Building, is within walking distance and is well worth the US$5 admission. Also, there are some interesting old colonial homes and other things to see on a walking tour of the Fort George area, which is safe as it is patrolled by tourist police.
Belize books and publications by Lan Sluder:
Belize First Magazine (http://www.belizefirst.com
Fodor's Belize & Guatemala Guide (new 4th edition coming this summer)
Adapter Kit: Belize (the first and only comprehensive guide to living, retiring, working and investing in Belize -- a best-seller on Amazon.com)
San Pedro Cool (the first and only visitor guide to Ambergris Caye)
Belize First Guide to Mainland Belize
UpClose Central America
Belize Book of Lists