Moonah is the closest suburb to the cbd ( less than 10km) where you can still get houses under 300k. It has a large stock of unrenovated 30s to 50s character houses which are being bought up or rented by the young and funky who cant afford anything closer to town. House prices in the neighboring suburbs on the city side, Lenah Valley and Newtown are a good 100k to 200k more expensive so it has great growth potential. Otherwise I would look at units/flats in solid suburbs like south hobart/north hobart and sandy bay.  There is a very high demand for rentals in the inner city areas.  Its a falling market down here so I would be wary of buying in the very cheap outer bogan belt of gagebrook/bridgewater/rokeby. Also while there is a lot of new infrastructure in kingston to the south, there seems to be an oversupply glut of  overpriced new housing and units. further south to huonville and this oversupply is even more pronounced. just my 2 cents.