Syracuse. I hate Syracuse as much as the next guy, but I think it'd be the matchup that'd garner the most national attention. UConn-Syracuse is recognized as a college basketball rivalry across the country and we have quite a bit of history against them.
Throw in the fact that these games could be played at Madison Square Garden and that Cuse has ties to a major conference (still tough to think about UConn as a mid-major, but we're not in a power conference and that's the harsh reality). Syracuse is usually a ranked team year to year, but as we all know they choke when it matters most. Along with Kentucky or Duke, Syracuse is the team I enjoy beating the most, and that's not something I'd want to give up.