Funny because my husband and I were just talking about this today - like if our son was a year older and at Navy this year, would he have been able to go? I'm not sure how it works at Navy, but at West Point they were called "trip sections" and you pretty much signed up for them. Rank had priority (so firsties would get to go before plebes) - for a trip section from WP to Syracuse to watch girls volleyball, probably anyone would get to go. For the AF football game in Colorado, you probably wouldn't get to go if you weren't a firstie or 2nd class. Usually travel was by military planes or buses, and the fees were very minimal (keep in mind this was 25 years ago, but I want to say we normally paid like $40 for a trip) including hotel and transportation and tickets in the cadet section (if it was a football game). Food was on your own dime.
I'll be interested to see what people say this is like today!