The most popular concert venue in the Palo Alto area is the Shoreline Amphitheatre. It's located on One Amphitheatre Parkway in the city of Mountain View, just south of Palo Alto. It's an outdoor venue so most concerts are held in spring and summer. It holds 22,000. The venue is laid out almost like a baseball diamond with bench seating in front and grassy area (general admission) in the back. It is auditorium style so seating in the front is low and towards the back is high. You can check out their event schedule at the Live Nation website.
Stanford Lively Arts
Founded in 1969 at Stanford University, Stanford Lively Arts produces and presents music, theater, dance, spoken word, and multi-media events. They place a special focus on innovation and risk-taking, and through commissions and premieres are an incubator and destination for new work. You can check out their event schedule here.