Hobart Airport (HBA) is 17 km east of the city, with frequent flights to Melbourne, Sydney, Brisbane, and direct services to Adelaide, Auckland, and the Gold Coast. There are no international flights other than seasonal services to New Zealand and Antarctic supply flights; most international visitors connect through Melbourne or Sydney. The airport shuttle bus runs to the CBD for around AU$25; taxis and rideshare are roughly AU$50.
The alternative is to come by sea. The Spirit of Tasmania ferry sails overnight between Melbourne (Geelong) and Devonport, about three hours north of Hobart by road. You arrive with your car, which is the practical way to do Tasmania — the island rewards road trips far more than it rewards staying in one city.
There is no passenger rail to Hobart. Coach services from the rest of the island use the Hobart Bus Mall in the CBD.