From Tavira you can ferry out to Tavira Island for a beach day complete with sit-down meals. Nearby, you can take boat tours to see dolphins and the Benagil caves. There are also a number of historic sites in town that are great for a walking tour.
You can rent a car to visit nearby towns, take the train from the center of Tavira, or book a bus trip. See the resources section below for more.
A note on footwear: the cobblestones are slick, all the time. Wear good walking shoes and avoid pointy heels whenever possible.