You could try Bonsoiree in Logan Sq/West Bucktown. On weeknights they have a 3 course prix fixe menu that works out to about $35 a person if you upgrade your entree. We like to think of them as a 3/4 version of Schwa. They have a patio in the back that could probably fit 20 - 30 people.
Their Saturday menu is a $55 prix fixe that's by e-mail invitation.
2728 W Armitage
Think Cafe on Western (near Fullerton) has terrific and sophisiticated Italian. It's BYO. The restaurant has several separate dining areas, so they may be able to accomodate a group in a private space.
For Spectra, if Latin/Mexican is OK, think about Los Nopales on Western (the bargain of the century, great specials) and Dorado (consistently excellent food, Mexican with a modern and eclectic flavor) on Foster. Both BYO, both have very nice and accomodating owners.
I think most of the good Thai places are BYO (Spoon, TAC, Sticky Rice, etc). Its not on the North-side, but Lao Szechuan in China Town was BYO last time I went (they previously served alchohol, so it might be good to call ahead fits to check). Also, Kan Zaman is a good BYO Lebanese restaurant in near north (around 500 N Wells St) with a Binny's within a 5 minute walk.
My best friend had a birthday party in the back room at Riques a year or so ago. It is BYOB, reasonable priced, and the food is yummy.
It changed ownership recently, but I understand the new owner doesn't plan to change anything.
Riques' Regional Mexican
5004 N Sheridan Rd
Chicago, IL 60640