There are two kinds of rivalries.
The first rivalry is one of location, for example UNC and NC State or USC and UCLA. This might be a fun rivalry for people that live in that area, but there isn't any kind of meaningful competition going on, and it means nothing to anybody outside those programs.
The second rivalry is one of competition. Think Yankees and Red Sox, or Syracuse and Georgetown, these rivalries are born from on the field (or court) competition.
Syracuse is never going to have the first kind of rivalry (this is a good thing, we are going to OWN the northeast).
When you look into your crystal ball to determine who our future rivals are going to be, look no further than our biggest competition.
Conference realignment is all about one thing, the big guys taking from the little guy. As we move along you are going to see a huge gap between the major conferences and everybody else. This means our future rivals are not going to be former or current Big East teams. They are simply not going to be on our level.
I see the ACC having four perennial powerhouse teams. Duke and UNC (no reason for them to go anywhere, again realignment is about making them even stronger). Syracuse (realignment has been great to us, I know things can change fast but as of right now there is not another elite basketball program anywhere in our recruiting hot zones) and Louisville.
Neither Duke nor Carolina seem like they will be our main rival in this new made-for-TV college landscape, because they already have rivals in each other. That leaves one option, Louisville, and possibly a second in Connecticut if they ever get picked up by a major conference (but honestly that possibility dwindles with every day they are left to wither in purgatory).