Do your research first by going on their website.
Do they offer the degree(s) your student is potentially interested in?
Where is the school located? If it is far away, do you have family or friends reasonably nearby in the event of an emergency?
What is the mission of the school? What is their focus? If the website shows them to be all about sports and your student is more focused on arts and academics, that may not be the best school for your child, and vice versa.
Do they offer advanced degrees in your student's field of interest?
Do they offer ROTC, if your student is interested in going into the military reserves after college? If so, which branch of the military sponsors the ROTC on that campus.
Look at their affiliations. Are they a state school, a religious school (and if so, which relgion / denomination), etc.?
Find out what accreditations they have. Some universities will only accept credits from schools with certain accreditations. If you don't see that on their list, ask when you call.
Look at their approved organizations. This can tell you a great deal about the makeup of the college or university.