Hey studentinrecoleta, tonight is not a good night to go out because elections are tomorrow and lots of bars are closed.
But here's some bars in Recoleta, with a brief description:
El Alamo: yanks and foreigners show up here a lot, but there are a lot of younger locals any day of the week. One of the few places in BA that's like a US bar. People seem to either love it or hate it.
Shamrock: Bar upstairs and small boliche downstairs. Nice spot to dance without the hassle of clubbing. I'd recommend this place as it's not quite the packed insanity of the Alamo.
Jack the Ripper: I think this place was all the rage awhile back, but has basically turned into a neighborhood pub that never gets too crowded.
Casabar: feels like a US sports bar. Nice if that's what you're in the mood for.
Milion: Mansion converted into a bar. Nice terrace out back. It has a bit of an upscale feel without being exclusive.
The Spot: A quiet place that's a bit off the radar. Pretty small. Good local bar vibe.
Gran Bar Danzon: Kind of a classy cocktail joint. The crowd is a bit older, so if you're a student, it may be best for a nice classy night out with friends, unless you're dying to meet the 40+ empresario of your dreams.
If you're kicking it solo and are in university, I'd go Alamo or Shamrock.
Just a heads up, there's not much of bar/pub culture here in the US/UK sense besides places foreigners go. It's more of a dinner with friends/drinks with friends/clubbing thing for the locals.
Also, outside of Recoleta, Sugar Bar in Palermo Soho and Gibraltar Pub in San Telmo are nice bar spots. Note, there are lots of places to drink in BA, but the mingly feel of a bar that newcomer would look for will have a lot of foreigners in it.
Hope that helps.
Oh, and being a female here alone. Watch out on the street. No need to be paranoid, but you might want to take taxis from anywhere you've been drinking until you feel safe and know the terrain a bit. If you're going out by yourself, you might want to watch out more for making fast friends with people you don't really know. The heightened risk in BA seems to me to be petty theft and muggings more than aggression that women alone need to worry about. I'm not a female, though. Just my $0.02.
On that note. Spanglishexchange.com, which organizes a language exchange most days of the week, is a great way to meet people who are also new to BA and practice your castillano. That plug sounds so formal, I should add I don't work for them or something. It's just a nice thing.
Have fun in BA!