One of the great things about the city during the summer is that its never really difficult to find a beer garden to enjoy an ice cold beer outside. Probably the easiest option is the Kaimono Koen (4jyo / 7chome) beer garden, about 7 minutes walk from the station straight up Kamiono Koen, on the right just before you reach 4 jyo. Great local brews from the Taisetsu Ji Microbrewery can be sampled as well as the standard Japanese favourites.
A slightly more conservative option is the beer garden at the top of the Terminal Hotel (next to Asahikawa JR Station). It suffers a little from not being street-level, but does offer a broad choice of food and drink as well as a festival-like atmosphere.
Which ever you decide on, you'll find it fun, relaxing and pleasant to be outside.
