Plaza Dos de mayo is right in the middle of the popular Malasaña neighborhood. This plaza is known for being the spot to do a “botellón”, or basically, a giant outdoor pre-game. On the weekends, between 10:00-12:30 at night, as long as the weather is nice, there will be tons of people here drinking beers, playing the guitar, and just chilling out until they head off to their chosen destination. One time I even saw an improvised flamenco show!
The rad thing is that there are things going on during the day here, too. Every weekend there is an outdoor market that sells all kinds of cool things, like records and CDs and other kinds of jewelry and knick-knacks. Once or twice a month there will vintage clothing and shoe stands as well.
Of course, the plaza is surrounded by different bars and restaurants that you can try. However, if you really want to experience the plaza in its true nature, I suggest heading on over on a Saturday night, buying yourself a Mahou and just enjoying the atmosphere.