Hanging out by the River
I don't live in Missoula anymore, but I lived there long enough to give some advice. And, I do still go back from time to time to visit my family that still lives there.
I would bring someone who has never been to Missoula to "Lunch in the Park" at Caras Park in downtown Missoula by the river.
Lunch in the Park was always my favorite thing, they have tons of different food vendors, great music, people everywhere, it is just an all around good time and a great excuse to eat lots of food! Missoula has a few unique shops in its downtown area which I miss and can't really find anything quite like them where I live now.
They are Butterfly Herbs and Bagels on Broadway. Also my favorite deli in downtown Missoula is Worden's Market. Fabulous food, beer and you can sit in there and eat and watch life go by outside. It's great.