Do you have to stay in the vicinity of Devonport? If not, hire that car and do some exploring. Are you into bushwalking? If so, there are some amazing walks up that way, lots of mountains and waterfalls, particularly around the Great Western Tiers. As others have suggested, Cradle Mountain is pretty close and worth a visit.
If you’re more of a coastal person, there are wonderful rocky walks along the north west. Drop into the Wynyard visitor centre to grab some geo tourism booklets and visit Rocky Cape. South of Devonport there are some magical caves around Mole Creek. The weekend of the 1 Nov is also the art and craft fair in Deloraine, if you’re more of a knitter than a caver.
In Devonport itself, visit the regional art gallery. It’s one of Tasmania’s best small public galleries.