Can't speak to Rio, but I just got back from BA.
There are a lot of leather stores around, 95% of it is cheap crap. There are several higher end options, however. Rossi y Caruso is by far the best in terms of quality of workmanship. It's pricey by Argentine standards, though still far below Hermes or even LV. They have a broad range of merchandise and all of it is well made. Another leather option is Casa Lopez. They use excellent leathers, but the workmanship isn't on the same level as RyC. It's still good stuff, though, especially for the price. I picked up a great weekend bag in black pebble grain leather from Lopez and am very satisfied with it. The designs at Casa Lopez tend to be a bit bolder and more innovative than those at RyC. Both brands have several locations around town.
In terms of food, in you're looking for just the Argentine staples of steak and malbec, it's hard to go too far wrong. There are countless options available in every neighborhood. In terms of more innovative restaurants, however, I must say that BA was a bit of a disappointment. I ate at several high end "foodie" restaurants, and while they made a good effort, the results fell a little short of what I would call truly great. And these higher end restaurants aren't that much cheaper than what you'll find in the States, either.
Be forewarned, most restaurants seem to do only one or two seatings a night. Service is very leisurely. Expect to have dinner no earlier than 10:00 PM and expect it last over two hours.
In terms of activities, there are a number of great clubs and bars, the names of which I unfortunately cannot recall because of the aforementioned availability of cheap and delicious malbec.
Two tips: taxis are very cheap, and the subte costs almost nothing. Getting around is extremely easy, although traffic can often be terrible, even in the middle of the night. Also, everyone will tell you to go to Avenida Florida. Don't. At least for shopping. There are some great street musicians there, but the shops usually contain nothing at all worth buying, especially the local leather goods.