My guesses (asterisks next to nominees I think could be displaced by the listed spoilers):
Best Play
Hand To God, by Robert Askins
The Audience, by Peter Morgan*
The Curious Incident Of The Dog In The Night-Time, by Simon Stephens
Wolf Hall Parts One & Two, by Hilary Mantel and Mike Poulton
If 5 nominees: Disgraced, by Ayad Akhtar*
*Potential displacer: Airline Highway, by Lisa D'Amour
Best Musical
An American In Paris
Fun Home
Something Rotten
The Visit*
If 5 nominees: It Shoulda Been You*
*Potential displacer: Honeymoon In Vegas
Best Revival of a Play
Skylight
The Elephant Man
The Heidi Chronicles*
You Can't Take It With You
If 5 nominees: It's Only A Play*
*Potential displacer: This Is Our Youth
Best Revival of a Musical
On The Town
On The Twentieth Century
The King And I
If 4 nominees: Side Show*
*Potential displacer: Gigi
Best Performance by a Leading Actor in a Play
Stephen Boyer, Hand To God
Bradley Cooper, The Elephant Man
Ben Miles, Wolf Hall Parts One & Two
Bill Nighy, Skylight*
Alex Sharp, The Curious Incident Of The Dog In The Night-Time
*Potential displacers: Jake Gyllenhaal, Constellations
Best Performance by a Leading Actress in a Play
Geneva Carr, Hand To God
Helen Mirren, The Audience
Elisabeth Moss, The Heidi Chronicles*
Carey Mulligan, Skylight
Ruth Wilson, Constellations
*Potential displacer: Renée Fleming, Living On Love
Best Performance by a Leading Actor in a Musical
Michael Cerveris, Fun Home
Brian d'Arcy James, Something Rotten
Robert Fairchild, An American In Paris
Ken Watanabe, The King And I
Tony Yazbek, On The Town*
*Potential displacer: Matthew Morrison, Finding Neverland
Best Performance by a Leading Actress in a Musical
Kristin Chenoweth, On The Twentieth Century
Leanne Cope, An American In Paris*
Beth Malone, Fun Home
Kelli O'Hara, The King And I
Chita Rivera, The Visit
*Potential displacer/6th nominee: Lisa Howard, It Shoulda Been You
Best Performance by a Featured Actor in a Play
K. Todd Freeman, Airline Highway
Richard McCabe, The Audience*
Alessandro Nivola, The Elephant Man*
Nathanial Parker, Wolf Hall Parts One & Two
Bryce Pinkham, The Heidi Chronicles
*Potential displacers: Matthew Beard, Skylight; Marc Kudisch, Hand To God
Best Performance by a Featured Actress in a Play
Patricia Clarkson, The Elephant Man
Francesca Faridany, The Curious Incident Of The Dog In The Night-Time*
Lydia Leonard, Wolf Hall Parts One & Two
Sarah Stiles, Hand To God*
Julie White, Airline Highway
*Potential displacer: Annaleigh Ashford, You Can't Take It With You; Judith Ivey, The Audience
Best Performance by a Featured Actor in a Musical
Christian Borle, Something Rotten
Kelsey Grammer, Finding Neverland*
Josh Grisetti, It Shoulda Been You*
Brad Oscar, Something Rotten
Max von Essen, An American In Paris
*Potential displacer: Andy Karl, On The Twentieth Century; Paul Alexander Nolan, Doctor Zhivago
Best Performance by a Featured Actress in a Musical (a.k.a. the most packed category, now two years in a row!)
Victoria Clark, Gigi*
Tyne Daly, It Shoulda Been You*
Judy Kuhn, Fun Home
Sydney Lucas, Fun Home
Ruthie Ann Miles, The King And I
*Potential displacers: Ashley Park, The King And I; Mary Louise Wilson, On The Twentieth Century; not to mention all of the ladies from An American In Paris and On The Town, Dee Hoty from Gigi, Nancy Opel from Honeymoon in Vegas, and the other two ladies from Fun Home
Best Director of a Play
Stephen Daldry, The Audience*
Marianne Elliott, The Curious Incident Of The Dog In The Night-Time
Scott Ellis, The Elephant Man
Jeremy Herrin, Wolf Hall Parts One & Two
Moritz von Stuelpnagel, Hand To God
*Potential displacer: Scott Ellis, You Can't Take It With You
Best Director of a Musical
Scott Ellis, On The Twentieth Century*
Sam Gold, Fun Home
Casey Nicholaw, Something Rotten
Bartlett Sher, The King And I
Christopher Wheeldon, An American In Paris
*Potential displacer: John Rando, On The Town
Best Choreography
Joshua Bergasse, On The Town
Warren Carlyle, On The Twentieth Century*
Christopher Gattelli, The King And I
Casey Nicholaw, Something Rotten
Christopher Wheeldon, An American In Paris
*Potential displacer: Graciela Daniele, The Visit
Best Original Score (Music and/or Lyrics)
Fun Home; Music by Jeanine Tesori, Lyrics by Lisa Kron
It Shoulda Been You; Music by Barbara Anselmi, Lyrics by Brian Hargrove*
Something Rotten!; Music and Lyrics by Karey Kirkpatrick and Wayne Kirkpatrick
The Visit; Music by John Kander, and Lyrics by Fred Ebb
*Potential displacer: The Last Ship; Music and Lyrics by Sting
Best Book of a Musical
Karey Kirkpatrick and John O'Farrell, Something Rotten!
Lisa Kron, Fun Home
Craig Lucas, An American In Paris*
Terrence McNally, The Visit
*Potential displacer: Brian Hargrove, It Shoulda Been You
Best Orchestrations
Christopher Austin, Don Sebesky, and Bill Elliott, An American In Paris
John Clancy, Fun Home*
Larry Hochman, On The Twentieth Century
Larry Hochman, Something Rotten!
*Potential displacer: Larry Hochman, The Visit
Best Scenic Design of a Play
Beowulf Borritt, Hand To God
Bunny Christie and Finn Ross, The Curious Incident Of The Dog In The Night-Time
Christopher Oram, Wolf Hall Parts One & Two
Scott Pask, Airline Highway*
*Potential displacer: Bob Crowley, Skylight
Best Scenic Design of a Musical
Bob Crowley and 59 Productions, An American In Paris
Scott Pask, The Visit*
Michael Yeargan, The King And I
David Zinn, Fun Home
*Potential displacer: Scott Pask, Something Rotten!
Best Lighting Design of a Play
Paule Constable, The Curious Incident Of The Dog In The Night-Time
Paule Constable and David Platter, Wolf Hall Parts One & Two
Jason Lyons, Hand To God
Philip S. Rosenberg, The Elephant Man*
*Potential displacer: Rick Fisher, The Audience
Best Lighting Design of a Musical
Donald Holder, The King And I
Natasha Katz, An American In Paris
Ben Stanton, Fun Home*
Japhy Weideman, The Visit
*Potential displacers: Kenneth Posner, Finding Neverland
Best Costume Design of a Play
Bob Crowley, The Audience
Christopher Oram, Wolf Hall Parts One & Two
Clint Ramos, The Elephant Man
David Zinn, Airline Highway*
*Potential displacer: Jane Greenwood, You Can't Take It With You
Best Costume Design of a Musical
Gregg Barnes, Something Rotten!
Bob Crowley, An American In Paris
William Ivey Long, On The Twentieth Century*
Catherine Zuber, The King And I
*Potential displacer: Ann Hould-Ward, The Visit