The Cathedral on Av. Alcalde between Av. Hidalgo and Calle Morelos is a good place to start. It was begun in 1561 and took about 30 years to complete. Dedicated to the Virgin of the Assumption, this Cathedral is easy to spot with its twin spires. The spires were actually destroyed in an earthquake (1818) and replaced in 1854 with the spires you see today.
Also of note are the 10 silver & gold altars which were gifts from King Fernando VII of Spain to thank Guadalajara for its support in the Napoleonic War.
Relics from the past - The Cathedral is home to the "Virgin of Innocence" located in a small chapel on the left as you enter. The story about this relic dates back to a time when large Catholic churches needed some sacred artifact to make it a holy place. Churches in Europe already had more than one John the Baptist head, duplicates of Apostle bones, and enough pieces of the "true" cross to fill a small forest. Lacking an established relic or remains of a dead Saint, they needed something else. So, the Roman Catholic Church came up with the bones of a young girl in 1786. The bones were sent to Guadalajara with a story about a young Christian girl who died while protecting her virginity in the 3rd century. Presto, a Martyr with a story that would make all love and adore this new addition to the Roman Church's list of pseudo-saints murdered by the Romans. Whether or not the story of how the girl who died 1300 years before her bones were pronounced holy was ever true is beside the fact. The fact is that if you say it long enough, history turns the story into tradition, and tradition becomes a historical fact which has no room for the truth. So no, there is no proof whatsoever to back up the story, but the faithful BELIEVE the bones to be those of a young girl which TRADITION says was killed while protecting her virginity.
Museo Regional de Guadalajara - Originally built in 1701 to be a seminary, this historic building has been a museum since 1918. The museum explores pre-columbian history through the Spanish conquest and includes some carriages from the 1800's and some paintings. Calle Liceo 60, Centro Historico. Entrance is $3 USD. Open Tuesday through Saturday from 9 to 5:30 and Sunday from 9 to 4:30.
While exploring the historic center with its beautiful buildings, fountains and monuments, bear in mind that Av. Independencia (near Plaza Tapatia) runs right past the Mercado Libertad. Look for the elevated pedestrian walkway that leads to it. The mercado is a must for shoppers looking for something to take home.
Things to Do in Guadalajara
Agua Caliente - A water park located at Km 56 on Carretera a Barra de Navidad, how long it will take to get there depends on what part of Guadalajara you are coming from, but it is around a half hour outside of town. The water park includes wave pool, water slides and restaurants.
Lake Chapala is close by and you should take around an hour to get there from most parts of Guadalajara.
Puerto Vallarta is a 4 and a half hour bus ride away, which makes it a nice beach destination within striking distance.