In my experience:
School Atmosphere - One of the biggest deciding factors.
Team Atmosphere and Culture - Another one of the biggest deciding factors.
Academic Reputation - I only visited top tier schools, so this was a given
Facilities - Minor contributing factor as most universities have amazing facilities. If they don't, then it's a good sign to go to another school
Major - Wasn't a huge determining factor as a) if it's an academically rigid school, then you'll be good no matter what major you are studying (unless you're going to be super-specialized) and b) most college students change their majors
Coaches Training - I played soccer, so it was less about their training and more about the 'vibe' I got from the coach: could I see myself having a positive relationship with this person for the next 4 years?
Location - had zero impact on my decision
Proximity from Hometown - had zero impact on my decision
Other contributing factors for me:
Weather - I'm a four season person, so I didn't look at any southern/southweastern schools. Duke was the most southern school I visited.
Alumni network - if their alumni are still involved with campus life and they have a large alumni group, then the chances of finding a promising career skyrockets
Intensity - not really sure how to put this into one term, but I knew going into college that I wasn't going to be on a World Cup team or get signed by Manchester United, so I wanted to enjoy my time playing soccer, but I was also realistic in that I wanted to make friends, do well academically, and enjoy college...not just have it be 4 years of nothing but soccer. So I wanted a coach and a program who appreciated that sport/life balance.