Not much in Logan. I know Moab Brewing has restaurant called the Beehive Grill. Not sure what beers they have there. Another option is Aggie's Sports Bar. They should have a decent beer selection. Cheers.
I echo the beehive grill and would also add White Owl, it is downtown. There should be around 10 Utah taps, plus other BMC craft (Blue Moon, Killians, etc. . .) and a bottle selection as well.