I've always been fond of the local Lincoln Park/Lakeview neighborhood establishments, but for tourists or people wanting to go downtown looking for a funky vibe, I always suggest Harry's Velvet Room. Martinis, decadent nibbles and desserts, plush decor...just a very nice atmosphere imo.
Keep in mind that I've never been a big clubber---just a drinker
so I tend to stick to bars without a dancing scene.