The first Sunday of every month, lots of bicycle riders gather 4:30pm at the Obelisco for an event called Masa Crítica, or critical mass (check here Protected content ). There is no planned path, it is decided at the moment. The movement is a bit anarchic and it has a great sense of freedom. Sunday, December 4, Protected content pm map Meeting point: at the Obelisco!
There's no organizer yet still works very well. The rides could be "long" (4 hours) but you are, of course, absolutely free to join or leave the mass whenever you want.
If you don't have a bike, you could rent one in one of this places Protected content Protected content Protected content
I don't know these companies; I just took the links from your favorite search engine!