I took my husband and some friends to Jasper for the first time in July '09 and we stayed at this place:
http://www.parkplaceinn.com/
It was really really nice and right in the heart of "downtown" Jasper so you're within walking distance of restaurants and bars for some unwinding after being on the bike all day. I would definitely recommend this place. Big, modern rooms, clean and reasonably priced, in my opinion.
I used to work in Jasper at the Fairmont Jasper Park Lodge, and while it's very nice there, it's a huge amount of cash just for a place to shower and sleep and it's away from the actual town of Jasper itself.