I would just stay in BA, personally. Tons of night life, beautiful women, great food. Stay in Palermo if possible. If company is paying for a hotel, stay at one in Palermo, I can offer a few recommendations if that's the case. If not, use airbnb.

Check out Teatro Colon, walk Palermo/Palermo Soho (which could easily take up a half day, or more). There are some day trips and guides that you can easily find online if that's more your style. Palacio Barolo is nice. Puente de la Mujer is beautiful, especially at night!
Find out if a soccer game is going on and see it.

If you like Polo, or think you might, Argentina has some of the best Polo horses and fincas in the world, schedule a tour, see a match, or even take a lesson, much cheaper than you would think. Truly a unique experience that you can't really get many other places. My brother and I used Polo Elite and thoroughly enjoyed it! We also went to see a match at a different arena, which was spectacular. Im sure there are other organizations that do the same, as well. polo lessons

One of the more fun activities we did was a pub crawl. I dont know if it's true, but the company touted that they were the only "real" organized pub crawl in the City. Whether it was true, or not, we had a great time. We met people from all over the world. I want to say we had a few free drinks in each bar we went to, had some food and beer when it first began, and the price included all of the covers. Pub Crawl
Just looked at the link for a second, it looks like they do them every night of the week now, when we were there it was just thur-sat, and I'd recommend one of those days regardless of what they offer.

Check out UBA, which is an ancient public university, my brother actually studied there. It's a bit...interesting. It's the leading public university (read: the only good one), and there is huge animosity between those that go there as opposed to choosing a private school, for some reason. Most of the people my brother met were extremely intelligent and upper-middle class- or very wealthy and chose it because of its' history.

If you have any more specific questions, feel free to ask. The vineyard tours suggested earlier are a great option. A guide is needed if you don't schedule directly with an owner, but a guide will possibly bring you to a few different ones. It will take up a whole day with travel time. You will have to catch a flight to go to the esteemed Mendoza, so it would take up two days, but there are some smaller vineyards a few hours outside of BA for the day trip, which is what I was referring to at first.

Also, if I have not mentioned, eat some facking red meat, it will amaze you.