Hokkaido trip in July

I am planning a trip to Hokkaido and have the following questions:

1)Please suggest hotels (with bath attached) in Furana, Biei and Hakodate

2) Any hotels with in-the-room onsen or hot bath in Sapporo, Otaru or Hakkodate?

3) What is the best way to get from Biei to Hakodate? If by flight, how to book for cheap flights? Is JUly considered a peak season and are there any cheap flights?

4) May I have the e-mail address of government tourist associations that I can write in for information.

Thanks so much

This hotel at Hakodate has onsen in the room. Nice view and veri nice too.

http://nagisatei.info/english_new/indexEn.html

Thot it is easier to travel by train in Hokkaido than using air.

Sapporo Hotel

http://www.b-norte.jp/norte2/english2.html

Cheap and nice too.

Otaru Hotel
http://www.i-reserve.info/authent/e/

What is the best way to get from Biei to Hakodate?

There is one direct flight per day between Asahikawa Airport (just outside Biei) and Hakodate. It is the fastest and most comfortable way.

If by flight, how to book for cheap flights?

The regular one way fare is around 17,000 yen. You could save somewhat by using a Star Alliance air pass, although its blackout period starts around mid July:
http://www.japan-guide.com/e/e2364.html

Is JUly considered a peak season and are there any cheap flights?

Yes, especially after around July 20, when the school summer holidays starts.