Behind the Cathedral, at the north end of Plaza Tapatia, is the Plaza de la Liberacion, with its huge fountain and statue of Father Hidalgo freeing the slaves in 1810 (the emancipation was actually signed in the Hospicio Cabana--seen at the south end of the Plaza Tapatia). The Plaza is lined with museums and public buildings decorated with murals by Jose Orozco, Guadalajara's answer to Diego Rivera.
The 400 year old Cathedral itself is certainly worth a look: it's a classic Mexican cathedral and contains some very nice sculptures and details, especially in the small side chapels.
The Palacio de Gobierno dominates the south side of the plaza and contains two Orozcos, one hovering over the delegate's chairs in the Congress Chambers and depicting the freeing of Indian slaves. You can go up on the roof of the Palacio, by the way, for a great view of the downtown.
On the north side of the Plaza is the Regional Museum, which is a sort of perfect little museum. It has a dinosaur skeleton, for one thing. It has a really comprehensive history of the area from the creation of the universe to present, with much relics and dioramas. Upstairs is a collection of modern paintings by important Mexican artists, many local, like the scandalous Zuniga.
At the other end of the plaza, the cupola'ed Hospicio Cabanas is now a cultural center with everything from concerts to lectures, to shows of film, photography and sculpture. The most impressive attribute is the ceiling mural by Orozco, the 'Four Riders of the Apocalypse'--a wild, violent work full of distorted figures and a brooding, blazing sense of justice and destruction--Orozco's masterpiece. To keep from straining your neck, they thoughtfully provide benches to lay down on while viewing the ceiling--and if you want to be more mobile, they have little mirrors for that purpose. Which is more than you will get in the Sistine Chapel.
From the Hospicio it's only a few steps to the Libertad Market, from whence you can cross Calle Mina on an elevated walkway and visit the Plazuela de los Mariachis. Sit for a beer and the roving bands of musicians will approach you to sing for an amount to be determined (you should be able to get them down under 30 pesos, around $3 US). If you like mariachi music, this is where it all started and is THE place to hear it--sort of like the Grand Ol Opry.