After spending a week here, my wife and I would highly recommend staying at Marius and Anita's apartment. The apartment is well appointed with quality modern appliances, fixtures and decor, yet maintains a fair bit of the original character and charm of the Circa 1800's building.
The location is very central to the CBD - there's a Woolies (supermarket), local pub (Tasmanian Inn - try the bangers and mash) and a few restaurants within walking distance.

Marius and Anita are great hosts who have created a relaxing place to stay that is warm and welcoming, they'll willingly offer any tips about Hobart and surrounds if you need them, and have supplied a fair few in the red folder

We will most definitely return in the future.