You've basically got 3 days in BA -- I lived there for 3 years, so here are some suggestions for sightseeing:
1. Explore at least three neighborhoods -- San Telmo, because they have a great street fair on Sunday, Recoleta, and Av. Florida (pedestrian street). A good guide book is "Buenos Aires Alive!". You can read while you sit at an outdoor cafe in Recoleta.
2. Cheap, good food: You can get an excellent steak sandwich (sandwich de lomo) at Bar Posadas, corner of Posadas and Rodriguez Pena, in a quiet part of Recoleta -- Outside seats too. El San Juanino is a block from there at 1515 Posadas @ Callao -- A small restaurant with excellent empanadas (little meat pies), roast chicken, and french fries -- all great -- this place is famous in the area. You'll have to eat a steak or two -- best in town (also expensive) is Cabana las Lilas in Puerto Madero. More reasonably priced: A cab ride away, in an area called La Costanera (riverfront), is "Los Anos Locos" (The Crazy Years). This place started years ago as a grill with seating under a tent. Now it's the most popular restaurant in that area, where locals go for a big family meal. Exceptionally good steaks. Tell 'em you're visiting and don't speak much spanish, and they'll take care of you.
3. If you want to see some good tango but don't have the stamina or $$ to sit through one of the many dinner shows/revues, here are 2 alternatives: (a) Cafe Tortoni, Avenida de Mayo @ Esmeralda -- every cabbie knows it -- This place looks like a stage set for Evita, worth seeing even without the tango show -- $10 cover for the Tango show in the back, with a $6 drinks minimum. (b) the Hyatt has a free 25 minute (2 dance numbers) tango show at about 10pm in the cafe. Timing is perfect for after dinner coffee. Call to confirm that it's on that night.
4. If you do take a day trip to Uruguay, it would be on Monday, to Colonia, not Montevideo. all told, it would cost you about $100. I strongly recommend (a) getting your hotel to arrange for an english-speaking guide/driver - might want to fax ahead for this, and (b) taking the fast ferry. Colonia is a town that passed between the Spaniards and Portuguese many times. It's now a UN World Heritage Site. Another way to explore there is to rent a moped, just inland from the ferry dock. I still recommend a guide for walking around the old town. It's a very sleepy place -- big contrast with BA, and that makes it interesting.
Here's a link with information:
http://www.expatvillage.com/travel/details/Colonia.cfm
5. 2 small hotels where we used to put company visitors -- so they're an OK standard for U.S. corporate travellers, but you won't pay chain prices: Hotel Park Plaza, Avenida Parera between Quintana and Alvear 011-813-4815-5028 - most staff speaks English, great neighborhood; Edificio Arenales Apartment hotel 4393-6882.
6. Argentine steak is very "beefy" tasting, but it's tough compared to the U.S. (it's very lean). If that's a concern for you, I'd recommend ordering Bife de Lomo (filet mignon), Brochette de Lomo, or Bife de Chorizo (like a strip steak)