There's a few options, people have mentioned Corner Bar, which is a nice option if looking for a more dive type place. Simple meals, hamburger baskets. I'd definitely recommend Bar 209, though, great food there. Other spots are:
For BBQ, there's CK Dudley's which has a lot of good stuff on their menu, lounge has a lot of TVs.
Another spot, close to the Bemidji State campus, is The Bunkhouse, which is a bar with grill options but also serves breakfast all day.
If you're in the mood for Irish, you'll want to check out Brigid's Pub. Only a couple TVs but offers a good selection of Irish food like Shepard's Pie.
Mi Rancho is a really good Mexican place with plenty of TVs and they'll get the game you want on in most occasions.
If you ever do want to fall back on a chain the main options for game watching include Buffalo Wild Wings, Applebees and the Green Mill.
Also second Bemidji Brewing, solid beer selection and amazing pretzels.