I think you'd enjoy going to Tigre for a day (independently or on a small informal tour). I've done this three times, once with a friend and twice on separate tours. I plan to join a local friend and my traveling partner and go there in October. We plan to drive and go to San Isidro first and onward to Tigre-- spend the day-- have a light picnic of wine and cheese and bread and fruits.

You can catch the train in town and go to Tigre on your own also. San Isidro is the stop before Tigre, if you go on a Sunday, there is a nice flea/antiques market right by the station.
You can rent boats and go out on your own or go on a larger boat tour.
There are many restaurants and some right on the water..
http://en.wikipedia.org/wiki/Tigre,_Buenos_Aires

You won't want to rent a car here, believe me, it is not what you think it is lol.

Go to Colonia for a day, by high speed ferry from BA. Come back the same day or stay overnight.

If you click on the name of a poster here - Marnie ... you can read her trip report and she tells all about going to San Antonio de Areco. You can get a lot of good information from her trip report... I will see if I can find it and just link it here for you ...

Here it is ... a great trip report and full of ideas ...

http://www.fodors.com/community/south-america/marniewdc-trip-report-3rd-week-in-bsas.cfm

Thank you both for your responses. This is all helpful information.

Scarlett, I appreciate the additional link you posted to the trip report, which I will read shortly and I will also look into Colonia for a nice day trip or possibly an overnight as suggested.

We will have about 5 days to explore surrounding areas outside of the 4 or 5 nights we plan to stay while in B.A. We are traveling with another couple who have not been to Buenos Aires before so we thought that amount of time would be appropriate for them to get a good overview of the city.

DJE

I'm hoppin' on this one!! I love how Scarlett can easily be understood. You should write a travel book Scarlett!

LOL,seeksocean .. Thank you.
Yes, I will write a book, something like .. Life in Argentina with Pup ... it will be a huge hit, everyone will buy it and read it to their pups. I will be sure to give you credit
But then you will have been here by then and will write your own book ! I had better get busy!!

Scarlett, I think the Pups Guide to BA (or you could call it 'The Ruff Guide to BA')is in order. Seeing BA through the eyes of Pup might be very timely for me. It's about time somebody wrote it from that perspective!

Meanwhile, my book may be all about the places I can't afford to stay at in BA and surrounds because my hard saved money went to some stockbrokers mega-bonus.

I think I may have to forget Punta Del Este.

I like the idea... Ruff Guide to Buenos Aires has a "ring" to it

You can stay in Jose Ignacio and spend a day in Punta del Este.. where is the name of that cool little hotel ?