If you're looking for somewhere to get your dance on, check out The Purple Tree Lounge right at the market. They have a good mix of music and a fairly timely bar staff.
For great frozen drinks, check out Wet Willies. I believe they're open during the day, so if you're looking for a day time way to chill out (with a kick) make a quick stop. At night, their drinks are still going strong, with an entire wall of frozen drinks to select from. My pick - "Call a Cab" - this drink is super-strong but mighty tasty. I recommend stopping by to pick up drinks. They have a dance floor, but the scene can sometimes get scandalous, as in, it reminds me of a dance club for 18 year-olds (it depends on the night though).
A whole wall to choose from at Wet Willies*
For a more laid-back, pub-style bar, check out Henry's right at the market. Not much to say - simple bar environment with a pretty darn quick bar staff. Usually not quite as crowded as some of the other bars if you're claustrophobic.
For something more sophisticated, check out one of the 2 rooftop bars. I can't remember the name of the one I've been to, but it's above an upscale hotel on the corner of the market and E. Bay St. They do have a dress code, so dress nicely if you want to get in. Further down the road is the rooftop bar at the Library. I haven't actually been here, but I've heard good things.
For the locals' pick, check out The Blind Tiger. It's several blocks down from the Market, so it's a bit harder to get to, but worth it. There's a small interior area, but a pretty sizeable, and nicely decorated patio in the back.
There are several other bars worth checking out, but you can only make so many stops in one trip, right?
*Picture from Wet Willies web site: http://www.wetwillies.com