Resident expert in the house. I used to cover Division I football, so I like to think I know a little something.
In college football, schools are in conferences, and based on where they end up in the standings, they go to bowl games at the end of the season if they have done well. For example, the bowl game that my alma mater's conference plays in is called the Rose Bowl. The top finishing school in that conference (the Pac-10) will play against the top finishing school in the Big 10 conference, and so on, so forth, with other bowls. There are some lesser bowls, and a national championship game (for the top two schools in the national rankings) but that's getting a bit detailed.
Anyway, I have always treated the Metropolis/New Troy colleges as being in the Big East, which would have them playing with other big East Coast schools such as Rutgers, Syracuse and Pittsburgh. So, based on that theory, if New Troy State finished first in the Big East, they would play in the Sugar Bowl, which is always played in New Orleans, on Jan. 1. They would play a school from the SEC (South Eastern Conference) which would be someone like Alabama, Georgia, Florida or Louisiana State. The SEC is a traditional powerhouse, so they'd likely slaughter someone from the Big East.
A side note: State colleges are usually the smaller school in the state (called land-grant schools; they belong to the state), so if you want New Troy to be a bigger school, I'd have them be New Troy University, not New Troy State.