There are various methods for getting into the city center (approximately 20 miles from EZE). My plan was to take the public bus for $2 but seeing that I didn't sleep the entire flight, I opted for a private car. The ride was $38 all inclusive (tolls, tax, etc). Not a bad deal but I've already blown my budget on the very first day!!!
Staying two nights at the Yira Yira Guest House. Paz, the owner, made me feel right at home. My room faces the street and I have a little balcony overlooking Uruguay street in Capital Federal. Great location, clean and keeps me close to the Retiro bus station and AEP airport for my travels around Argentina. And, for $35 a night, you can't beat it!
After checking in, I set off on foot around the neighborhood. This city has a lot of energy and some seriously crazy drivers! Pedestrians DO NOT have any right of way here. You really have to keep an eye out even while crossing at a green "walk" sign. Cars really don't give a crap that you are in the sidewalk.
There is one other solo female traveler staying here at Yira Yira. Her name is Rachel and she's from Canada. She has been in BA for nearly a week and was most recently traveling around Columbia. Off to dinner with Rachel, maybe some tango and more BA exploring.