Spreckels Organ Pavilion, Balboa Park

You can watch a free concert at the Speckels Organ Pavilion in Balboa Park! It is a spectacularly beautiful semi-circular outdoor pavilion built in Italian-Renaissance style. Organ concerts are every Sunday at 2pm, and summer concerts are Mondays 7:30pm from late June to Labor Day. Some Sundays at 2pm they have a family show (see their website), and other nights they have operas. There is a nativity scene in the pavilion at Christmastime. The pavilion is lit up beautifully at night, as is much of the park.

It's nice to sit in the shady side wing of the pavilion, though during concerts it's not ideal because a loud tram goes by every few minutes. The entire organ pavilion is also affected by very loud airplanes that fly overhead every five minutes, so concerts can be a little difficult. But the overall mood is blissful in this beautiful place.
People come here to get glamorous wedding and quinceanera photos.
After, you can eat at Craft Cafe near Mingei International Museum, or Panama 66 near the Museum of Art. Both are counter-service.

Directions

Parking: The Organ Pavilion parking lot, at the intersection of Pan American Rd East and President's Way, gives you good access to everything and holds a lot of spaces. Parking is free. The Veterans Museum also has a large parking lot that is free and a short walk to everything. 
The Alcazar parking lot is awesome as it's right by the Museum of Us in the main square, but it's often full unless you come early.
Spreckels Organ Pavilion Concerts, Sundays all year long 2pm, free. Mondays 7:30pm late June to Labor Day, free. 
Craft Cafe, outside Mingei Intl Museum, open 8:30am to 5pm daily. Lunch served till 3pm.

Click on map for interactive view