I recently went to the Feria de Mataderos in Buenos Aires. This resembles other fairs in Buenos Aires but offers more local products at a cheaper price and is less overrun by tourist (like for instance the fair in San Telmo). Additionally the fair features folklore dancing and Gauchos showing off their ring lancing skills. If you do not have the time to go country side this will be your best change in seeing some Gauchos and get a glimpse into their culture without having to leave to Buenos Aires.
How to shoot the Gauchos
The Gauchos start their competition around 15:00 o'clock. The fair starts at around 11:00 o'clock. So if you arrive around noon you have plenty of time to go over the fair and get something to eat. About 30 minutes before the competition they will prepare the street for the competition. This is the time you want to go towards the competition area to get a good spot. If you want to take good pictures I would recommend to find a pot a little bit behind the goal with the ring. The riders will race down the street and try the pierce the rind with a tiny lance. Make sure that you have a wide enough lens with you. The picture below was taken with 18mm lens on crop sensor camera.
Additionally you want to bring a long lens with you to take the some detail shoots. The picture below was taken with a 105mm on a crop sensor camera. It is important to freeze the action of the riders. Those riders are incredible fast and you will be really close to them. I had to stop down my camera to 1/4000 of second and the riders in some of my pictures still have quite some motion blur. It will take a while to get your timing right to capture the riders in the moment and location you want them. It took me properly about 30 minutes before I got the shoot below, right in the moment the rider pierces the ring.
They have plenty of rings and sometimes if a Gaucho gets the ring he will give it a way to a spectator in the crowd. Overall the Gauchos are fairly nice and have no problem with you taken their pictures.
As mentioned this fair has much less tourist. The main reasons for this is that it is less well know and it is quite far away from the touristic areas of Buenos Aires. To get there it will properly take you about 1 hour with public transport from any mayor tourist area in Buenos Aires. You can check their webpage to see which buses go there. Most likely you need to connect.