What sort of activities, other than the bullfights, are associated with the holiday?
The traditional thing to do is going to the Pradera (Prairy) de San Isidro, besides Manzanares River, just opposite Vicente Calderon Stadium (metro Marques de Vadillo), where a fair is held. To be true, not too interesting, crowds of people and bars and food stands. There it is the Ermita de San Isidro and the Miraculous Fountain, where you'll see lots of people queueing to fill a bottle of its water. If you have nothing better to do, take a walk there just to see the ambience. A few people (mostly kids and elder people) wear the traditional madrileño dressing.
Apart of that, there are some concerts and other 'modern sort' activities. The program can be found at
Madrid Municipality Website , clicking on the San Isidro banner of the home page.