I think the real wildcard is the People in the Picture - just because there's been so little known about that show.
I agree that Catch Me and Book of Mormon are definites. I have a strong suspicion anything without an original score is going to have a hard time getting a nod for best musical this year. Also, like several posters upthread, I think the voters are sick of jukebox musicals as well so a good jukebox musical will probably only get nominated if a lot of the original score shows suck. (Ie, if everything else turns out to be floptastic as Wonderland looks like it's going to be)
The only closed show that might get a nod would be The Scottsboro Boys but if The People in the Picture opens strong, I don't even see that happening. I think Sister Act is very likely, not a "lock" like BOM and CMIYC are but still very possible.
The fourth spot depends entirely on The People in the Picture - if it's good, that'll be the fourth nominee. If it's bad/a disaster that'll open the door for either The Scottsboro Boys or Priscilla.
While I personally LOVED BBAJ, the only nomination I could see that show getting is Benjamin Walker being nominated and considering how long the show has been closed and all the buzz of the current/new shows, I don't even see that happening.
2010: Next to Normal (May 25), Hair (Jun 9), American Idiot (Sep 10), Bloody Bloody Andrew Jackson (Sep 26), The Scottsboro Boys (Oct 17), Fela! (Nov 14), Next to Normal (Dec 30)
2011: That Championship Season (Feb 15), La Cage Aux Folles (Mar 16), The Book of Mormon (Mar 16), Anything Goes (Mar 30)