So many great things happening in that neighborhood!  Here are some of my favorite bars.  I hope you like Bourbon (or whiskey in general)!

• Cantina -- small nice trendy'ish bar with creative craft cocktails
  
• Tradition -- awesome speakeasy'ish place without needing a password or anything.  Don't remember if they ever got a sign/purposely didn't get a sign, so just look out for a door guy in a suit.  Great sazaracs and other old timey drinks.
  
• Rye -- another cozy spot for creative craft cocktails
  
• Rickhouse -- speakeasy'ish place.  They have a photo album sized menu of cocktails.  Sometimes has live music.
  
• Johnny Foley's Irish House -- this place is more of a pub for your run of the mill cocktails and beer.  On a Saturday, there might be a cover charge and there will someone playing the piano there.  Always very lively.
  
• Jasper’s Corner Tap and Kitchen -- love this place for a late night bite and cocktail.  They're part of the Kimpton hotel family, but they're so much more than just a hotel bar.  They have a pretty sizeable cocktail, spirit and beer menu.
  

I don't know how walk-happy you two are, but if you're feeling a little more adventure, either walk or cab to North Beach (I do this walk all the time!) and hit up places on Columbus Ave.:

• Tosca Cafe -- If it's a cold night, warm up with a hot coffee or chocolatey cocktail here.  They have menu for hot cocktails.
  
• Comstock Saloon -- Speakeasy'ish place with food and old timey cocktails.  One side's a restaurant and the other's a bar.
  
• Bocadillos -- I love this place.  It's a Basque restaurant so they serve cuisine from the border of Franch/Spain.  I sometimes come here after dinner for dessert and a drink.  They have a nice cider, beer, and wine menu.  They serve tapas in case you want a late night snack.
  

From North Beach, you can also go for a walk along The Embarcadero.  Everything will likely be closed after dinner time, but it's still a nice walk.

If you're into clubbing at all, in Union Square, there's Ruby Skye and Infusion Lounge.

If you want to check out dive bars, head to Tempest.  Huge warehouse-looking bar, sometimes with a live band, and super cheap and stiff drinks.  Word of advice -- walk there from the 5th St. side of things, not 6th St.  5th St. is super high end with Bloomingdales and Nordstrom and all, then things somehow go very south by the time you get to 6th St.

Another good bar near there is Monarch.  Really great cocktails and sometimes an acrobatic show right above the bar.  Free photobooth.  For a cover charge, there are usually DJs spinning downstairs.

For another dive bar, there's The Showdown.  This is on 6th St., but very close to Market St.  Only walk there from the Market St. side of things.

If you want to check out another neighborhood, I highly suggest the Mission District.  Let me me know if you want any recommendations there.  Have fun! :)

One of the best bars I have ever been in is  Bourbon and Branch  You have to get reservations.  It is a very cool speakeasy.  I also like  Rickhouse, House of Shields  http://sf.eater.com/archives/2012/11/27/13_iconic_san_francisco_dive_bars.php#more

You should check out  Cantina or  Local Edition (691 Market St). And if you like it even fancier,  Press Club (20 Yerba Buena Ln). It's a bar and a lounge, not a dance club. Have fun!

San Francisco is a great place to experience fantastic Jazz and Jazz clubs. Try Cafe Du Nord, Top of the Mark at the Mark Hopkins Hotel, and the San Francisco Jazz Center. Also not to be missed is see anything at Yoshi's San Francisco on Fillmore Street.

A lot has been mentioned by prior posters, but you might want to go to the   The Independent for live music.