If you want to know what teams a school fields, Wikipedia's articles on the various conferences have tables showing the men's and women's sports the leagues sponsor and the ones in which each school competes (example: Syracuse is the lone ACC member that doesn't field a baseball team). Some schools compete in sports not sponsored by their conference—perhaps most notably, the SEC does not sponsor men's soccer, so any SEC schools that wish to field a men's soccer team must do so in another league. Similarly, the ACC doesn't sponsor hockey, so Notre Dame's men's team competes in the Big Ten and Boston College's competes in Hockey East. (The articles include tables showing where schools' teams compete when their main conference doesn't sponsor a sport.)
That's the sort of thing for which Wikipedia is probably reasonably reliable because there's not a lot of reason why someone would want to vandalize that sort of material.