Yep Ive been there, 4 years ago. Its a great place for a visit and this makes me think I need a new job. Anyway couple things to make sure to check out are:
1) The cemetary in La Recoleta, its probably the biggest attraction the city has to offer and will take about half day to walk through it all. I believe its the biggest above ground cemetary in the world and is a concrete maze of mausoleum full of famous people like Eva Perone and other Argentine elite. Fantasic, and beautiful definatly like nothing you have ever seen beefore. It is also in the middle of the La Recoleta are which is a trendy touristy type spot, with lots of little shops cafe's and parks, this area alone is worth a walk around.
2) La Boca. Its down by the water in a poor area but its a great tourist spot and has some famous architecture and brightly painted buildings. The buildings are so bright because the poor there used leftover boat paint to paint there houses.
3) Soccer! Look into going to a soccer game. I didnt go in Buenos Aires, but I did go in Rio and Ill say that there is nothing quite like experiencing a soccer match in South America.
4) Italian Food, yes Italian food. Argentina is a Latin country but Buenos Aires is made up of something like 70% Italian descent and they are famous for their Italian food there. I heard it is better than Italy and in my limited experience from Rome I would say they have a good argument.
5) BBQ. Thieir beef in that country is arguably better than you will find in Texas. Reason is that their cow population went feral at one point then was redomesticated and everything is grass feed hormone free. Eat lots of beef there, its fucking delicious. My personal recomendation is Siera la Boca, its an all you can eat Argentinian style BBQ right on the waterfront.
6) Empanadas, eat them for meals and snacks. Yum.
7) Colonia De Sacramento, skip it unless you are desperate for another passport stamp. Its a very cute tourist town filled with American expats, that can be reached by a ferry ride from the port. Ferry ride is 2-3hours each way and given your time restraints I would say Buenos Aires will keep you very busy. There is nothing to special about Colonia other than some resturants, shopping, and pituresque views that make it a romatic quite place to be enjoyed with the Mrs.
8) Watch your ass there. There are a lot of poor in Buenos Aires, they do a good job off hiding the citys poverty in the tourist spots, but the poor hood rat kids prey on tourist there. I got robbed by a group of kids when some sneaky lady in a wheel chair demanded my attention at a cafe, after she left my bag was gone.
9) wine, they are famous for the Malbec there, if you drink wine make sure to get a bottle or seven.
Thats all I can think of off the top of my head. Dont be off put by some of the locals either though, they are famously snooty there, just how they are so dont get all offended. One more thing I would add is that if you can swing some extra time in the area you should try to get to Icguazu national park, 2 hour plane ride north on the Argentina and Brazil border and it is one of the most amazing places I have ever been in my life, a definate bucket list item. If you can do it you only need one full day in the park, which is all about waterfalls and jungle. The waterfalls there make Niagra falls look like a leaky faucet, it is so emense and amazing, its almost undescribable so Ill add a few pics
