(With thanks to Madison Heslop, who conducted the research.)
Hopsmith Tavern (15 W Division St, 8 minutes from the hotel) is a pretty standard but quite large pub with tvs for sports fans, offers discounted specials on different drinks and foods each day of the week between 5pm and 4am on weekdays and nearly all day on weekends. There are a lot of bars and pubs on this block of Division.
Hash House a Go Go (1212 N State Pkwy, 10 minutes from the hotel) offers huge servings of brunch and burgers, plus the restaurant has a bar with happy hour from 3-6pm every day. They are particularly known for their Bloody Marys.
Clark Street Ale House (742 N Clark St, 13 minutes from the hotel) has a good range of tap and bottled beers as well as whiskeys and free popcorn. They have daily specials during happy hour (starting at 4pm).
Kerryman's Irish Bar (661 N Clark St, 16 minutes from the hotel) has a lot of space and the virtue of also being a restaurant, but it's a bit more upscale than the others listed, with happy hour from 4-7pm.