In Belize, we went on the cave tubing, it was great! It also allows you to get a bus ride throught the country and town. I would not recommend going into the city unless you are with a group or tour. It is very depressing and poor- with not much to do. The guided tours are your best bet.
In Progresso/Merida, we went to Chichen Itza (mayan ruins) that was very interesting. This is also a long bus ride (@2 hours one way), but again, worth the time and money. These ports are new for the cruise lines and do not offer much shopping. The beaches are marginal.
If you are going to Cozumel, you can shop there and find time to snorkel as well. We had a great time on the Pride this year! Going again in May (eastern carribean)