The most famous place in Furano is called Farm Tomita. The best time to go is in July when the Lavender is in full bloom. I was there in late August and there was still some flowers and lavender in bloom, but if you can, go in July.

Biei is most famous for the rolling hills and trees that have been in famous commercials. If you don’t rent a car, a good thing to do is take the “twinkle” bus. There are two different routes, the flower route and tree route. Both routes go to about 5 different locations and you can get off at some of the places for about 10 minutes to take photos and some places you just drive by. If you want more time or don’t want to be on a schedule you really should rent a car for Furano and Biei as the good places tend to be spread out.

For more information please see the Japan-Guide.com.
Here is the Official Biei Homepage.
Here is the Official Furano Homepage.