We have been to Buenos Aires twice. The first time, we stayed in the Crillon:
http://www.tripadvisor.com/Hotel_Review-g31274 1-d306767-Reviews-Crillon_Hotel-Buenos_Aires_C apital_Federal_District.html
In spite of the negative reviews we were quite happy with it. If you do your research of the different districts of Bs As, you will find that it is well placed for the shops etc. We found the staff helpful and there was free Internet access. There are lots of Internet "shops" in Bs As and they are VERY cheap.
The second time, the tour operator no longer offered the Crillon and put us in the Waldorf:
http://www.tripadvisor.com/Hotel_Review-g31274 1-d455745-Reviews-Waldorf_Hotel-Buenos_Aires_C apital_Federal_District.html
Although not far from the "action", the imediate area wasn't so nice.
We also stayed at the Tres Reyes for one night because of a diverted flight. This is definately too far from the shops.
If you want a dinner and tango show we can't rate El Querandi highly enough:
http://www.querandi.com.ar/