The holiday inn downtown isn't too far from downtown and the bars... but brew pubs are a little ways.. the closest would be Tamarack (new one downtown on Front St) maybe 4 blocks from your hotel or go accross the higgins bridge and the Kettle house is near 4th and Higgins (maybe 6 blocks from your hotel).. But to get to Bayern it is a ways across town on Russel St and Big Sky is way out by the airport (free tasting there only no buying drinks as they are too big now).
My advise though if I were you I would skip all of them and head south of Missoula on 93 to Stevensville 30 min drive and go to the Blacksmith Brewery and when you finish there keep going south on 93 to Hamilton and you'll find my favorite place ever... Bitterroot Brewing. Good Luck! :rockin: