We don't want to spend the entire 10 days in the city but don't want to spread ourselves too thin either. What suggestions?
Dont know what kind of a budget you are on, but no doubt that the most spectacular option would be to catch a flight to see iguazu falls - 2 days to visit the falls is enough, its a great break from the city landscape, and its really unbelievable over 10 years ago
I'm guessing you've already been to Bs As and back by now. If not, and for others who might look to this post for answers, I suggest taking a day and going to El Tigre. You can get there by train on the Mitre line from Retiro terminal for only 1.35 pesos (~40 cents US).[The train is nothing fancy--a lot like a New York subway train--but its only about 45 minutes] You can take a nice tour by boat around the river delta region for about 40 pesos ($10 US), rent a kayak, visit some nice shops, and eat at waterside restaurants. It's still part of Buenos Aires province but you'll feel you are far far away from the big city. There's a visitor center at the train terminal that can give you information.
There are El Tigre tour packages available at several locations in Bs As, but check out the prices and decide what best fits your comfort level and budget. We felt very safe on the train and got all the information we needed for a fun afternoon in El Tigre.
The two earlier responses look good too. We went to Iguazu. You can do the park with the falls in a day and not feel cheated or rushed. You should at least the night before or after your visit, or both. We stayed at the Hostel Bambu Argentina and it was great. (Be careful in booking as there is a Hostel Bambu on the Brazil side as well.) The town of Puerto Iguazu is fun. I recommend the Tango Bar for a beer and entertainment, and El Quinche de Tio Querido for dinner.
Didn't go to Uruguay but heard from others that it is very nice. about 10 years ago