I really enjoyed shopping in Cozumel. My favorite store was Los Cinco Soles (The Five Suns). There might be more than one Los Cinco Soles store. The main one is in dowtown Cozumel (San Miguel). Within that main one is the restaurant Pancho's Backyard. It is considered to be one of the best restaurants in Cozumel.
I can't give you any first hand advice on diving, swimming and snorkeling. All I can tell you is that people who dived, swimed and snorkeled in Cozumel said it was great; especially regarding Chakanaab National Park.
I never been to Belize. Sorry I can't help with that destination.