So here's my very arbitrary list of things to do in Buenos Aires - I give this to everyone who ever asks, "do you recommend?..." - so this is a quick cut and paste job. BA is a city very close to my heart.
Let's start first in Buenos Aires, since that's the city I know best:
If you like to eat meat...
Hapening or Miraflores for good meat, in Pueto Madero the newest part of BA, nice and with that meat packing district feel, good for a stroll along the river
Oviedo, international food with the best wines, (Beruti 2602) in the stately neighborhood of Recoleta.
El Desnivel, for a standard parilla with heart, in San Telmo
Now, if you want to eat like a Porteño for real...
Pippo, which is this great Italian old school restaurant for the work a day crowd. Its got everything from parilla to milanesa?s, and home made pasta. I highly recommend the ?super vermicelli con tuco y pesto, which is homemade vermicelli half with pesto sauce, half with bolognese and then topped with grated regiano, mmmmm. This place is in the part of BA called Congresso, by the obelisk, and its located on Montevideo 341 b/w corrientes and saramiento ? great for a lunch when you?re waling around the city center.
El Cuartito best pizza in town! located on Talcahuano 937 b/w Marcelo T De Alvear and Paraguay again in the noble neighborhood of Recoleta. Or Guerrín is good too, that?s on Corrientes, Av. 1368 ? eat standing up like the Argies do, and don?t forget to order you?re pizza with a Moscato (a kind of wine).
AND don?t forget to eat ice cream, which is an Argie specialty. Freddo?s, you can?t go wrong.
And if you?re up for a typical libation, as for a fernet with coca cola ? I think this drink sums up the porteño character.
Also, definitely eat lots and lots of facturas!! Mmm...media luna de grasa? Yes, please!
For places to go and things to do...
San Telmo, con negocios antiguedades y locales ideal ir a la plaza San Telmo los domingos/sabados cerca del medio día
If you?re going to look at the Casa Rosada/Plaza de Mayo (go on a thurs, see the madres de plaza de mayo do their march), then you could also take a walk to Congresso, the Obelisk and then Calle Florida ? that would pretty much take care of the city center
Palermo Viejo, Hollywood and Soho, great boutique shops, little restaraunts, bars ? I love this area and inevitably always end up here
La Boca is nice, if you want to see a slice of history, is kind of touristy though ? unless you go to the Bonbonera to watch a futbol match! Naturally, get on the Boca hincha, its amazing!
Recoletta is beautiful too, with more upscale everything. Beautiful houses and apts. with the Recoleta/Chacarita cemetary which is definitely worth a walk around.
Also, you should consider going to El Tigre. If you're lucky you can make friends with someone who has a house out there (ours is rented out, sorry)
As for the rest of Argentina:
Argentina is HUGE! Cordoba and Mendoza are great areas to visit. Especially Mendoza since its so close to Chile. I?ve never been, but have been dying to go!
As for Iguazu, its an amazing place to visit too, with its waterfalls and jungles. Being that its so close to Brazil though, you might want to check if its rainy season, which could make touring difficult ? although we were in Brazil (Bahia) in May and it rained sometimes, but was insanely gorgeous all the same.
Another place you can visit, though, is Salta or Jujuy, which is the desert region to the North and still maintains much of Argentina?s indigenous past. These places really can only be visited in winter/fall (it gets bloody hot).
As for gyms. Fuck if I know! LOL!
Also, don't let anyone tell you that BA is dangerous. Its not anymore dangerous than any other urban place.
Suerte!! And have a great stay. I'm sure you'll never want to leave