I'd suggest Frenchmans Cap is a good alternative to the Overland Track.
Although it can be done in less time, 4 nights would allow plenty of time to explore.
Suggested itinerary:
Day 1 - car to Vera Hut (a fairly long day & potentially muddy through the 'sodden loddens').
Day 2 - Vera Hut to Tahune Hut, probably only half a day.
Day 3 - summit of Frenchmans, swim in Lake Tahune (cold), explore the area, take photos, relax.
Day 4 - Tahune Hut back to Vera hut (again, probably only half a day).
Day 5 - Vera Hut back to the car.
This is a very moderate itinerary really as it can be done fairly comfortably in 3 days.
Other suggestions:
Lake Rhona (2 nights plenty to go in, a day to explore the area, a day out).
Pine Valley-Labyrinth area, Cradle Mountain - Lake St Clair NP (spectacular camping at Lake Elysia).
Wall of Jerusalem area (very easy access, could spend more time exploring surrounding areas).
Mt Anne Circuit (maybe a bit more demanding tho for an inexperienced walker).
I'd suggest you grab a copy of John Chapmans
Cradle Mountain Lake St Clair & Walls of Jerusalem National Parks guide book or his
South West Tasmania guide book depending on which part of the state you want to go to, plenty to chose from in those 2 books.
Enjoy your stay if Tasmania is your chosen venue