There are a ton of bars in and around Downtown and the Financial District. I am rather partial to the Cigar Bar and Grill, not so much because of the cigars, but more because of the live salsa band and dancing. Lots of fun.
If you want a more traditional bar experience, try the Comstock Saloon or the Old Ship Saloonl. Both are great for just grabbing a drink and chattin your date up.