Drummond makes some good points about Equal Opportunity laws. Alas there are a few problems:
1) Schools that expressly state an age preference are generally outside the reach of the jurisdictions mentioned (US federal and NYC municipal law). Of course, other jurisdictions have similar EO laws but they also have their own set of exemptions.
2) Virtually all schools in the US are aware of the law, public perception of what the law states, and the unseemliness of denying admission based on age. Accordingly, they will not state their reasons for rejection explicitly. Regardless, trying to prove that age was a significant motivating factor behind rejection (if indeed that was the case) would be an extremely difficult undertaking.
Many schools have internal policies that prohibit discrimination based on age:
"All decisions concerning an individual's admission to or participation in any University program must be based on that individual's qualifications, free of stigmatizing consideration of race, color, national or ethnic origin, religion, disability, gender, sexual orientation, marital status, age, citizenship or Vietnam era or disabled veteran status."
Columbia University