Would like to add my voice to the chorus of those who've thanked Gaucho100k and others (GUWonder comes to mind) for all of the useful information in this thread.
My wife and I are on our 5th day in BA now, on a two week honeymoon. We're in the Hilton until tomorrow (on an award stay) and like the Puerto Madero neighborhood just fine, and cabs are plentiful and it's easy to get to other neighborhoods. (Although it can be a bit worrisome the first few times one is with a driver who lanesplits between other cars - usually we just see motorcyclists doing that in the states.
It's high season now, and finding affordable hotels for the rest of our staty was a bit tricky, but we're going to try a budget B&B-style place in Palermo called Casa I.F. Studio Rooms. Stopped by there and the staff were very friendly and the rooms seemed decent enough.
I'll agree with others that walking is the way to see the city. So many beautiful neighborhoods - one can be in Greenwich Village one moment and Montparnasse the next.
We'll be headed to Uruguay for a few days on Monday (checking out the Four Seasons, who had a pretty good rate including spa treatments etc.) and we're trying to figure out what to do with our last three days in the area next week. Had considered seeing Mendoza for a couple of days, but Aerolineas Argentina appear to want US$600 each for airfare, so that's probably out. Will contact the folks at Wow Argentina recommended elsewhere in the thread to see what they might suggest as side trips.
The only disappointment so far has been dinner at Cabana Las Lilas. My club steak was ridiculously over salted, my wife's baby beef came medium well instead of the medium rare she ordered, and waitstaff were a bit overzealous in taking away plates before we were done eating from them. I will give them kudos on the wine selection, however. Upon requesting a recommendation for Malbec, the waiter found a 2002 DV Catena which wasn't even on the list, and that was quite excellent.
Tonight we're headed to El Mirasol, which has good reports on FT, so we'll see how it compares.
At any rate, I'd certainly recommend a visit to just about anybody.
Cheers