If you're closer to Ogilvie, you're not far from Avec, which is open until 1 or 2 on weekends, I believe.
Closer to Union Station and the Clinton Blue line, you could head 5 or so blocks west and hit Jak's Tap. Open until 2/3am on weekends. Good selection of beer, better than average pub grub.
Also a little bit west, though not as far as Jak's, I'm guessing there are a few spots in Greektown that would be open. Artopolis, perhaps?
My other thought was the hotels in the area - JW Marriott and W City Center and the Allegro are all within a 10 or so minute walk of Union and Ogilvie - but I don't know if those bars/lounges would be considered reasonably priced.