In Sapporo i´d recommend to try getting food in Susukino (the night district). I remember there beeing a good Ramen shop and a good sushi shop inside the building with the ferry wheel on top.
In Furano i went to a small restaurant wich served a special kind of Okonomiyaki. I think it was called Masaya (wikitravel says its 5th Street (between Furano Marche and Furano Station). The owner was very nice and spoke good english because he lived in Canada for a year.
For Furano i´d say max 2 days should be ok. Besides the farm this is just a normal town. In Sapporo it depends what you want to do. I´d say 2-3 days.
There is Noboribetsu Onsen not to far from Sapporo. Its quite famous with Japanese and a bit pricy. I didn´t like it as much as other places because it was quite touristy and expensive but its ok and the only place i can think of near Sapporo or Tokyo. It has alot of funny statues, a geyser that erupts every 3 hours or so, alot of hotels to choose from and "Hell Valey" wich is the natural volcanic area with steam everywhere and stuff. See my
blogpost for some pictures from there.
Other than that my second recommodation is Aiku Onsen just outside of Sendai, but i guess thats to far to travel.
Hope that helped a little
Edit: Actually i´m sure now that the place in Furano was called Masaya and it serves Teppanyaki, take a look
here. If you do read Japanese
this is the restaurants page.