Well, I can't exactly comment on Asahikawa except it seems inevitable that you'd arrive here if you're moving from one corner of Hokkaido to another. Say, from Wakkanai in the North to Membetsu in the East.
Asahikawa is most well known for its ramen so there I went, on one of my eating rampage (well, not exactly - only had one bowl of soyu ramen).
Then, walked around the shopping malls towards the central park to work off the hearty lunch.
Had much fun watching squealing kindergarten kids on their excursions in the park. That's actually very healthy activity - kudos to such activities.
From the central park, you can catch a glimpse of the river flowing through Asahikawa (namesake probably) as well as some mountain ranges (not too sure which ones - but I doubt it's the Daisetsuzan). The scenery's not too bad.
Otherwise, the town's a little sleepy.