The Imperial Room happy hour is one of my favorites downtown. They have half priced apps and half priced martinis from 4-7 pm. So when you have the desire for a classy cocktail but don't feel like paying $10 head to Imperial Room. Most martinis run for about $4.50! You can't even get a rail drink at that price downtown.
Rosen's across the street from the Imperial Room also has an amazing Friday happy hour. If its been one of the longest weeks, than head to one of the longest happy hours in town. $3 on all beers on tap (including Guinness!) $3 on almost all cocktails and it lasts from 4-10 p.m.
Keep it cheap, but keep it classy Minneapolis!