Tasmania is a relatively untouched part of Australia in terms of tourism. While I was living in Australia, we have decided with few friends of mine to go and visit this beautiful place just 1 hour and 20 minutes flight from Melbourne. The tickets price are really really cheap, you can get a return tickets for 50-60$ with Jetstar.
The best way to go around the Island is by car, once landed in Hobart international Airport hire a car straight a way in the airport, the city centre is just a 15 minutes ride. Hobart and Southern Tasmania offer plenty of things to see and do if you are looking for a weekend, you can find everything here, from fantastic food and wine restaurants to some stunning scenery. Hobart plays host to a variety of festivals and cultural gatherings as well as being home to MONA, the famous museum of old and new art.
If the weather is good, you can drive up to the Mount Wellington (1,271 metres above the city), just 20 minutes drive, and you will have a stunning view of the whole Hobart, make sure you take some warm clothes as the temperature will drop around 10-15 degrees up there, will be an awesome experience. 
If you are in the city on a Saturday, Salamanca Market and the Victoria Dock are always fun to explore and have lunch/dinner, we have been to the Mures Lower Deck restaurant to have some fish and was delicious. Instead, if you have some extra days to spend around the area of Hobart, I recommend to do a 3 hours cruise in Bruny Island, one of the most stunning wildlife destinations in Australia and/or if you are in Tasmania between October and June you can do a 2-hour scenic boat tour and have the chance to see dolphins, albatrosses and whales on their migration.
After spending two days in Hobart, we started our trip driving along the east coast with a first stop in Bonorong Wildlife Sanctuary to see Kangaroos, Tasmanian Devils, Wombats, Koalas and many others. Then after a short drive, we moved to some of the most gorgeous places to visit in Tasmania Swansea, Coles Bay and Freycinet National Park that have stunning landscapes and beautiful white sandy beaches, when visiting Freycinet National Park you can expect the entire walk to take over 3 hours.

After that we kept driving along the coast to the town of Bicheno, this is a perfect spot to spend a weekend during the summer months with plenty of great places to swim in and some great divings as well, the water is not really warm though.
Continuing the drive, at the north end of the Eastern coast there are the towns of Scamander and St Helens and the stunning Bay of Fires with its red rocks.
The Bay of Fires stretches over 50 kilometres from Binalong Bay in the south to Eddystone Point in the north. This beautiful stretch of Tasmania’s east coast has been named by Lonely Planet as the hottest travel destination in the world, and is generally one of the most beautiful places to visit in all Australia.

All our overnights were in campsites, we didn’t book anything in advance, we slept all the time in tents, very nice and for sure cold experience even if was summer time in Tasmania. Here, you can spend an all day exploring the Bay of Fires if you do an overnight in St Helens or Binalong Bay, you can get a campsite with an incredible view and just enjoy it.
After that we went to Launceston in the north, the northern end of Tasmania has become an incredibly popular destination in recent years for wine lovers and mountain bikers.
Moving north west we stopped at the iconic Cradle Mountain and Montezuma Falls, if you are a walker this one will be in your bucket list as well. In the same area there are the massive Henty Sand Dunes, that are reaching heights of around 30 m.
The last stop of our trip, on the way back to Hobart, was Mount Field National Park (less then 2 hours driving from Hobart) which is one of Tasmania’s oldest national parks and is also one of its most diverse with stunning landscapes, great walks, rich wildlife and the star attraction are Russell Falls, really beautiful.

We spent in Tasmania a total of 5 days, in my opinion are not enough to fully enjoy this amazing Island, if you like to walk, hike and get lost in the nature you can spend easily over 10 days.