[Firebird]

I felt that Noboribetsu is a bit overdeveloped and there are no budget places in Town (no minshuku or ryokan in low price class). cheapest started around 8000yen without food.
But if you want to do only a short trip i guess its the best bet because its close to sapporo and so close to the airport and not to far from Honshu.
The Shinkansen end in Hachinohe wich is why it takes around 10 hours by train to get up there.
You might want to take a place or find a night train.
oh, there might be a ferry service from Toyko to around sapporo!

Around that area is the lake Toya-ko wich has fireworks every evening, another onsen, a nice lake-side area and a place wich didnt get restored after a volcano eruption and looks like it got bombed. I would suggest renting a car for that area. There is a youth hostel but its a bit outside of the city

I although enjoyed the rugged coast of muroran. There is a youthhostel from wich a nice walk along the cliffs go to a cape. otherwise Muroran is a pretty ugly industrial town.

By the way, does it have to be Hokkaido? The nicest onsen ive been is 1 hour from Aomori (Tohoku) in a Ryokan. The Ryokan is outside the city and there is a beatifull hike nearby. The Onsen is huge and everything is dark wood. The water is milky and it is mixed bathing (so dont be shy) but there is an hour only for the girls. The ryokan is 5000yen without food (there is a kitchen but no restaurants near by!) and 10000yen with food (my friends said the food was amazing). If you book the ryokan before you go there will be a free bus from aomori.
The good thing would be that you can be there in 4 hours by shinkansen and a bit express train. Oh that place is called sukayu onsen!