I know bars weren't on your radar, but the Mark II is open till 4:00am every day and it is currently the best late night pool option on the north side of the city. It has one very decent free 8' with tight pockets, lots of room around the table, and a very friendly and seriously enthusiastic pool crowd (folks bring in their own cues), especially between 1:00am thru 4:00am. It's only 2 blocks south of the Evanston Chicago border on Western Ave. so you could easily cab it home for about $10. It's not easy holding the table there and late night, it is a great place to go.
It is best to get there between 1:30 and 2:00 am if you want to get a chance to play. There will probably be only 3-4 people waiting to play. Most other places close at 2:00 and there is always a light night surge. after 2:00 there will be as many as 12 or so people signed up on the board waiting to play. Warning though, this place can get smokey.
A nice little daytime secret is Cary's at 2251 W. Devon. It's a bar with another free (sometimes they ask for a two drink minimum) and very decent 8'. It opens around noon and you'll likely be the only one on the table in the early afternoon. The nice secret is that there is free parking in the back. So if you get thirsty after playing at Pressure, this is an option worth checking out. It is in the middle of a very crowded East Indian neighborhood and you will think you're in another country until you walk through the doors.
Good luck and enjoy your trip!