It's a college town. 
Is it tho?
From my perspective Billings is an industrial town, with either 2 or 3 refineries in town. Mostly blue collar.
If you're going to be there 3 weeks then you must eat at the Montana Brewing Company restaurant and try all their beers. I like the Sharptail Pale Ale. If you have weekends off and don't mind a drive you should head up to Lewistown, MT, and eat at the Mint. It's small town fine dining at it's best. The artichoke chicken is great, the walleye too. Can't go wrong with a steak, either. Also might drive over to Bozeman and check that out. I've strolled through campus once but can't really recommend anything.
Also if you're into history you should check out the Battle of the Little Bighorn site down by Hardin. (Don't actually go into Hardin though, and if you do, watch yer topknot.) Be sure to stay on the trails, or watch out for rattlesnakes, they're all over.
Sadly the second best restaurant in Billings is probably Uno or some crap.
Let me know if any of this piques your interest and I can recommend more or offer more details. Oh also you could get a day of fishing on the Bighorn River, should be fishing well by now for sure. Maybe go up to Roundup and shoot some prairie dogs?
I see Billings as sort of the gateway to the rest of MT. I just swing through and top off the tank and pick up the last of the supplies and GTFO of there.
