If I had to guess, Duke will play OSU or Purdue.
If it's the former, no idea where the game will be played. If it's the latter, it'll be in Durham. Duke played in West Lafayette 2 years ago.
Over the history of the challenge, Duke has played as many home games as road games. In fact, every single team in both conferences is either +1, even, or -1 in terms of home vs road games. It appears they really look at that as a criteria as who gets a home game the following year. Since Duke is even, it could go either way. Remember that before this year, Duke played 2 consecutive road games in the Challenge so it's entirely possible Duke gets 2 straight home games.
As for the Champion's Classic, much of Kentucky Nation just went into complete hysteria because they get a shot at Duke in 2 years. So many of their fans have an unhealthy obsession with Duke. It's pathetic. UNC fans hate Duke but do so with some level of dignity, not to mention they're actually THE rival of Duke. Haven't figured out the non-stop obsession with Duke on the part of many, many Kentucky fans. Also, it's not just the fans. It's the players and Cal as well. Cal explained their poor performance against WV in the Elite 8 last year to their anticipation of playing Duke. This is the exact quote:
“Do you know how badly we wanted to play Duke?” Calipari said. “I think that’s why we played so badly against West Virginia. We wanted Duke so badly we couldn’t see straight.”
By the way, Duke had yet to play Baylor in Houston when Kentucky lost to WV.