There are some craft shops in that area of town -- along North Front Street, near Memorial Park and near the Tourist Village.
Some people also set up craft stands on the days when cruise ships arrive. Check here for the cruise ship schedule:
http://www.belizetourism.org/component/option,com_remository/Itemid,56/func,select/id,58/
The zoo is about 29 miles from the City. You can get there by bus, but you need more time than 2 hours (50 minutes each way plus a couple of hours at the zoo). The easy way is by taxi, but that might be expensive.
http://www.belizezoo.org/Here are a few other ideas, but these places are outside Belize City too...
http://www.howlermonkeys.org/http://www.bacabecopark.com/http://www.oldbelize.com/index.php?section=1