The union in the Kleinbasel is very spacious and light and they have a few rooms one can rent (though it's quite expensive). Here's a list of their rooms:
http://www.union-basel.ch/union/raeume/index.php.
For something really classical, you should try one of the "Zünfte" (guildhalls). The main two would be the Safranzunft (Falknerstrasse,
www.safran-zunft.ch), which has several really beautiful old rooms and a huge hall, and the Schlüsselzunft (on Freie Strasse), which was recently renovated. I'm not sure if they have rooms to rent, but there is a restaurant.
If you need something slightly cheaper, the Volkshaus at Claraplatz has several extremely reasonably priced rooms...but they're not particularly attractive.
There's also a great space above the "bar mitte" in Gerbergasse, but I'm afraid I can't remember the name. You just go into the Mitte and up the stairs to your left and you're there.
Happy room hunting