In my opinion, the cheapest public transportation in our city are the busses. I think they are a great option not only for their cheap prices or large range of routes, but because there are a few green busses in circulation and you might get lucky getting to travel with one.
The subways are by far the fastest. They don't cover all the city, but if you want to get somewhere quick and escape traffic, I recomend going with it. The prices are also quite low.
