Haha, imagine that. When you said a lot of bars in the downtown area I had a fleeting thought that you might be here. Turns out to be true.
OK, here goes:
Molly Brown: My personal favorite. It's kind of a misfits bar but not really. Good vibe, lots of pool tables and probably the best beer selection of all the downtown bars and is definitely the best spot in the Barmuda triangle.
Haufbrau: At night it's a crowded hippy bar with loud performances, not bad when it's more chill, and it's cool for a visit since you're doing a pub crawl. They have excellent burgers during the day. Check em out sometime, during lunch hours.
Scoop: Possibly the sketchiest bar in town by word of mouth. But is mostly fine just not with the best selection of brew. Also looks the worst from the inside.
Bacchus Pub: Awesome hang out pub, can be crowded sometimes. Good bartenders and staff with a good selection. Popping by here first would make sense since it's the absolute first in the downtown bar scene.
The Cannery: Not bad but not the best, decent selection and usually very nice bartenders. Good for one drink.
The Plonk: Has a reputation of being the "hipster" bar, but is actually pretty good and has an avant garde feel to it. Great bartenders who can make some of the best mixed drinks in town. A little more expensive than other places, but not by a lot(like one dollar more maybe).
The Copper: One of my other favorites with the Molly and Bacchus. Great bartenders and great selection for whiskey. Some are expensive but for good reason. I'd definitely check it out since it has a nice vibe and is probably the most chill bar in town.
The Crystal: Famous and/or infamous for their happy hour. Which depending on when can be a little bit too crowded. It's decent, not the best by any stretch of the imagination but definitely should be a part of any pub crawl here.
Finn: Tries to be classy, I have to admit I haven't drank there since it used to be Santa Fe Reds(which was a shitshow that I've been to on too many occasions). Looks chill from what I've seen.
Rockin R Bar: Dear god, could be the second worst bar in town. Crowded as hell during weekends with the worst of the worst you think of when you think college town. I used to spend a lot of time there before most of the international kids I hung out with moved back to their respective countries. Can be a lot of fun though, as I've enjoyed my time there before. Don't be surprised if the waitresses and drinks suck, though.
The Legion: I like the bar almost solely cause I befriended a bartender on one of my pub crawls and he gets me free drinks all the time. It's a good bar to hang out in despite the claustrophobic lay out. I'd check it out.
Bar 9: Known as the worst bar in town and where you have the highest chance of being roofied. Douchebag frat boy central. I'd experience it if I haven't before. But if you avoid any bar in town, it should be that one.
317: It's cool, check it out. Nothing special but that's all I can say really.
The Pourhouse: Meh, check it out since you haven't. But I never really cared for it. It does have tables and waitresses so if you just want to chill you can.
Zebra: Cool bar, but usually has a cover change since there's always a band playing. Never worth it when there's a cover charge. Otherwise, yeah check it out.
Colonel Blacks: Personally love it, probably the only bar in town that serves absinthe. Great vibe and has two lounge areas where you can just chill out on a couch. Check it out.
The Eagles: A friend of mine bounces there. It's mostly a bar for the older crowd and looks old as hell. It's the other veterans bar along with Legion. It's worth checking out in my opinion since it's the only bar in Bozeman with a real dart board.
As far as bars not in Downtown bozeman:
Cat's Paw: Go in with a group if you can. As you may know anything on north 7th is shady. It's decent but mostly for the guys coming in from the trailer parks, if that influences your decision.
Mixers: Country bar which is pretty decent, a little farther away from pub crawl lengths.
Specs: Ok sport's bar that has ok food. Not much else to say.
Hide-A-Away Lounge: Very chill and cool sports bar with good food.
Hope that helps.