Back when it was established in 1935, the Universidad Autónoma de Guadalajara was the only private university and medical school in the whole of Mexico! It now boasts some 16,000 students, and a large contributor of highly qualified medical graduates in Mexico, bringing a certain amount of prestige to Guadalajara.
The UAG campus is found in the west of the city, though it has a number of different buildings for different classes, year groups and so on. There are plenty of exchange programmes in addition to their medical school, so hopefully you can find something there which works with your degree.
The University of Guadalajara has one of the most open and welcoming policies toward international students of any university in the world. If your home institute is a partner of UDG, then you can partake in an exchange. If not, you can study as an independent student and come along anyway!
In addition to those in and around the city, UDG has campuses spread out all over the State of Jalisco. Its primary campus is in the heart of the city, while the others are dotted around all over the place, totalling up over 250,000 students in total. There is a range of opportunities in terms of programmes for international students, though you may wish to contact the university about your specific situation.
The Monterrey Institute of Technology is a behemoth of a school, with 90,000 students across 31 campus in 25 cities in Mexico! The Guadalajara campus is like a world onto itself, with loads of sports and socializing opportunities away from the city centre. The university is off to the north west of the centre, so you might want to look for accommodation in that general direction.
There are degree programmes for undergraduates, masters and doctorate-level candidates, though since it’s a private university it will cost more to study here than a public institution like the University of Guadalajara.