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Museum of the Army and Air Force
Originally a barracks and military academy, the facility was renovated in the late 1990s and opened in 1999 as a museum documenting Mexico's military from its evolution from a colonial Spanish army to its complex and evolving role in providing for the national defense. 15 galleries highlight historic conflicts while providing displays of flags, uniforms, tanks, jeeps, artillery and other military equipment.
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Instituto Cultural Cabañas
This UNESCO World Heritage Site east of Plaza de la Liberación is a cultural and art center where the fresco paintings of Jose Clemente Orozco are exhibited.
The official name of this small triangular plaza is Plaza Pepe Guizar, named for the composer who was responsible for the song "Guadalajara". However, its popular name comes from the mariachi bands who, for a small fee, will serenade you while enjoying the restaurants and bars around the square (a word of warning, though: this neighborhood becomes sketchy after dark). The Plaza de los Mariachis is where the famous Mexican Hat Dance (Jarabe Tapatío) was born.
It sounds tacky, but this wax/oddities museum can be an interesting way to learn about Jaliscian history.
Jalisco Philharmonic Orchestra
One of Mexico's top professional orchestras, the Jalisco Philharmonic celebrated its 100th anniversary in 2015. The orchestra performs three full seasons of classical music from January to December each year under the direction of Jose Luis Castillo. The orchestra frequently tours abroad. The concert hall is a showcase of opulence that will be appreciated by students of music, architecture, and history.
Palacio de Gobierno
This is the historical center of the government of the State of Jalisco. Today it is mostly visited for its murals, the work of the famous Jalisciense artist, José Clemente Orozco. The most famous of these is a huge portrait of Miguel Hidalgo in the vault of the old chambers of the State Council.
This plaza features two large cup-shaped fountains and a gigantic sculpture of Miguel Hidalgo, the man who signed the Mexican Declaration of Independence in the current Governor's Office. It also serves as an atrium for the oldest surviving theater in the city, the Teatro Degollado, and it's the usual spot for massive free concerts.