We are spending 2 nights in Hobart in late March and are looking for accomodation that is fairly central.

Hobart is small. Central Hobart is smaller. At this moment, I'm staying in Battery Point which is a five minute walk to the docks.
Decide on what you want to see. Look at where these are on a map. Then decide on what suits you.

While in Hobart check out the Cascade brewery tour. but book ahead on line or by phone since its sold out a lot. nice walk from Hobart central you pass many convict era sites.

You just need to realize " budget" could mean different things to different people. I'm a cheapskate so for me, budget means anything up to $35 p.p.

Quality Hotel Midtown at $140 a night, for two, has own bathroom, and is central, has a restaurant downstairs, and also walkable to Subway etc.
Its on the Quality Hotels website.
Have stayed at this one.

The Waratah Hotel is about as central as you can get, wi-fi and breakfast and double room will set you back between EUR55-70 depending on your dates. But it is budget. I stayed there once a few years back (I'm fancier now!) and it was good value and it is the best price for central. The Quality Hotel mid-city would be another - never stayed but I know someone who has and they were fine with it. There's a Travelodge as well. I always linger in Tripadvisor before booking any hotel.
