There are lots of stuffs you can do while in Cebu, whether you're staying in Cebu as a transient or as a tourist. Here are some activities you might want to consider to have the most of your stay here in Cebu.
Island Hopping Beach Outing
Bird Watching Horseback Riding
Nature Trips River Tour
Spelunking /Cave Exploration Heritage Tours / Museums
Church Pilgrimage Race and Marathon
Shows and Concert Strolling in Parks
and lots of other things to do.