Depends - you say Tasmania, but where are you planning to go, and for how long in each? It's not uncommon for tourists to drive 2000km in 2 weeks in our little state, and it'll take longer for you to drive than it would on that darn northern island.
Anyways, if close to Hobart, Mount Wellington you'll find bloody cold for astro! And potentially be in the snow and wind too.
South, areas around Howden are popular for auroras as there are a couple bluffs that are exposed to the south/south east. South east, on the Tasman Peninsula are some good spots. Mount Pleasant Radio Observatory, a little east of Hobart, has good conditions too.
Depending on plans shortish drives on the Midland Hwy might suit you. Not huge amounts of traffic at night, about as flat as you get in Tassie, and some old towns you might be able to get night shots of too.
Let me know if you're after more info!