The center of town has a lot of action during the day and a little bit of action during the night. It features Congresso (congress building), Plaza de Mayo, Casa Rosada (like the white house in the states), the Metropolitan Cathedral, the Oblisk (located on 9 de Julio), and the world famous Teatro Colon. You can walk up and down Avenida de Mayo from Plaza Congresso to the Casa Rosada (or vice versa) in about 25 minutes without stopping. While you are walking from Congresso to Plaza de Mayo you will cross over the world's widest street, 9 de Julio. By the time you go half way across the street the light changes, and you have to wait about 3 minutes for the light to change to be able to cross the 2nd half of the street.
Subte (Metro)
The supte runs up and down Avenida de Mayo. You are able to hop on the subte right by Congresso and take it all the way to Plaza de Mayo. There are four stops in between these two destinations that allow you to get off and see different locations. If you have time I would just suggest to walk the streets, because there is a lot of stuff you can see in such a short amount of time.
Food
There are a lot of cafes and restaurants that are located up and down Avenida de Mayo. Most of them have seating outside during the day and into the early evening. Most of the restaurants will close down in this barrio at about 7pm, because a lot of the their business is from the workers who commute to the center of town. There is a mom and pop sandwhich shop that I went to about every other day that is located on Avenida de Mayo and Uruguay (in between Avenida de Mayo and Rivadavia). You can't miss it because there is always a line coming out of the store during lunch time. They have all different types of sandwiches, but I think the best sanwhich is their milenesa completo! A sandwhich here is only 3.40 pesos (just over $1 Us Dollar). There are also plenty of pizza parlors in El Centro that sell empanadas and pizza by the slice. Of course, don't forget that almost every restaurant sells steak!