Kale Sartor
Google
This hostel is great. A lot of people stay for long periods of time, so even if you're just there for a few days (like me) you pick up on the sense of community and comradery that they keep going. And the staff are just as social and involved as the guests, all intermingling and hanging out. They have events, but there's also a lot of chill down time, and plenty of space to find a quiet corner to do your own thing. Huge kitchen, paid laundry, nice TV, book nook, fireplaces, couches, chairs, and booths, pool table, info about the area, etc. And it's in a great location walkable to much of Hobart.
Accessibility note - like most hostels, the main building is not accessible. However, there is a back building with accessible dorm rooms, and they are happy to help make it work, though if you can't do any steps at all you couldn't access the kitchen, laundry, lounge rooms, etc. Still could be a good cheap stay if you just need a bed for a few nights.