Keys to Buenos Aires

Recommendations
Visit Recoleta Cemetary and then shop in the market outside the Cemetary.
Shop in San Telmo on Sunday.
Buy amazing leather goods at the Murillo Streat Leather District, especially Murillo 666.
Take a tango lesson.
Enjoy a tango show. We went to Esquina Carlos Gardel. The food was terrible, but the show was amazing. Eat before you go.
Argentine beef. Skip the pasta and anything else on the menus. We loved La Brigada in San Telmo and La Estanciero in Palermo.
Mendoza Malbec.
Despite being touristy, a meal at Cabaña Las Lilas in Puerto Madero is really good.
Experience Las Madres on Thursday afternoon at the Plaza de Mayo.
Have a drink at The Alamo/Shoeless Joe's when you need to speak English to someone, anyone.
Hang out for a few hours at an outdoor cafe, drinking and talking. We liked La Biela and so did a lot of other tourists. No matter.
Gelato.
Take a side trip outside the city. We didn't and I wish we had.
Rent an apartment with bytargentina, unless you need the services of a concierge or your sheets and towels changed daily (there's nothing wrong with that!). If you stay in Palermo, make sure it's a central location and the apartment has internet access.
Buy ten boxes of Havannets. Then buy ten more and stuff them in your carry-on at the Duty Free Shop.

Anti-Recommendations
Don't bother:
Visiting La Boca. Definition of a tourist trap.
Waiting to get into Cafe Tortoni. The pretty interior doesn't make up for the disgusting food and complete lack of ambiance.
Getting hyped about Palermo. It's a great neighborhood, with plenty of restaurants and boutiques, but there are no bargains to be found here.
Booking the services of Laura Chummers for tango. We were really disappointed by our experience with her.
Skip Galerías Pacífico. It's an impressive mall, but it's still a mall.
Eating anything but beef was a disappointment. The rumors of a booming culinary scene are a little overstated, I think.
Studying the guidebooks. We got some good suggestions and information from Frommers and Lonely Planet, but we also got some really bad advice, especially restaurants and the tango tourguide who didn't live up to the hype she received in Frommers. Word-of-mouth on the Internet is going to be a lot more helpful. Check out chowhound for restaurant recommendations.

These are all my opinion, of course, and based on a whopping eight days in BA. I'm no authority, just an opinionated photoblogger.