1. Have to play regularly, ideally with stakes
2. Geographic proximity preferred
3. Can't displace an established in-conference rivalry
Utah and USC (or Utah and Oregon for that matter) have played a bunch recently for high stakes, but lack all the other factors. In particular, both those schools have established in-conference rivalries (UCLA for USC, Oregon St and Washington for Oregon)
Colorado has no in-conference rival and is geographically closest to Utah...but the two teams have never really played an important game.
So here's the list of Big 12 teams we WON'T have a bitter rivalry with:
TCU, Baylor, Kansas, Kansas St, Cincy, West Virginia and probably UCF.
That leaves Texas Tech and Oklahoma St (who will likely, but not definitely) be rivals with one another, Iowa St, and Houston.
My guess is TTU, Okla St pair up and Houston ends up about our level so is the best bet for a natural rivalry