Jay Pritzker Pavilion in Millenium Park a landmark in Chicago. Some timeless music has played here. Musicians / Bands like Brad Meldhau, Wayne Shorter, The Chicago Symphony Orchestra, and Brian Blade and played here. Some of the events you have to see are the Chicago Jazz Festival, Chicago Blues Festival, and the Chicago Gospel Music Festival. The venue is a HUGE outdoor field with an incredible stage. It seats thousands of people and can fit a full sized orchestra on stage. Also, you're amidst Chicago's incredible skyline and within walking distance of the Chicago Art Institute. If you're up for nightlife you can walk to TONS of bars and clubs. You're literally right in the heart of downtown Chicago.
