While everyone else is walking around the antiques fair in San Telmo and picking up items that are too big to take home, head to Parque Lezama, a public park in the same district. The city of Buenos Aires was first founded here by Pedro de Mendoza (see his statue in the park) in 1536. In 1857 it was sold to Gregorio Lezama whose widow ultimately gave it to the municipality of Buenos Aires in 1894.
The park borders a part of what used to be the Rio de La Plata, before its course was redirected and the neighborhood of Puerto Madero was created. And while Buenos Aires is almost completely flat, this park, along with the Plaza Francia and Barrancas del Begrano are on a rise that sets them higher than the rest of the city. There are rustic paths for walking and biking and a few lookout points over where the river used to be.
Also in the park is the National Historical Museum of Argentina, established in 1897. It holds a collection of some 50,000 pieces, some of them dating back to when Argentina was a viceroyalty in the late 1700s and continuing until 1950.