I still haven't seen Outsiders or Hell's Kitchen, but I think my final predictions are (roughly in order of what I think the likelihood is):
Best Musical
Suffs
Days of Wine and Roses
Illinoise
The Outsiders
Water for Elephants
Hell's Kitchen*
* honestly could see a tie getting this to 6 nominees, with the Heart of Rock and Roll also a surprise possibility
Best Play
Stereophonic
Prayer for the French Republic
Jaja's African Hair Braiding
Mary Jane
Mother Play
* on the bubble: Patriots
Best Score
Days of Wine and Roses
Stereophonic
Suffs
Harmony
The Outsiders
* also possibly a tie in this category, as I haven't seen Outsiders but Water for Elephants and Notebook both seem to have "equal" scores to me (though I'd rank W4E slightly higher)
Best Book
Days of Wine and Roses
Suffs
Illinoise
The Outsiders
The Notebook
* I wonder if Illinoise not being a traditional book musical could hurt it in this category but I think the effort to make a cohesive story out of the album is a feat in and of itself. I wasn't enamored with The Notebook, but it seems to be respected by a lot of people, and the other option here would probably be W4E
Director
Maria Friedman - Merrily We Roll Along
Rebecca Frecknell - Cabaret
Justin Peck - Illinoise
Alex Timbers - Here Lies Love
Jessica Stone - Water for Elephants
* I...really don't know what's going on in this category outside of Merrily so these are mostly who I thought had the most interesting visions (the critics didn't like Frecknell, but it seems like general sentiment is warmer). It also seems like Michael Grief should get a nod somewhere, in which case my bet would be Wine and Roses but I really have no clue
Choreography
Illinoise
Water for Elephants
Heart of Rock and Roll
The Outsiders
Hell's Kitchen
* hard to tell since I haven't seen HK/Outsiders, but I could also see Cabaret or even Gatsby getting into this category. Heart of Rock and Roll probably also isn't as secure of a nomination but I thought it was one of my favorite parts of the show.
Best Actor in a Musical
Jonathan Groff - Merrily We Roll Along
Brian D'arcy James - Days of Wine and Roses
Eddie Redmayne - Cabaret
Chip Zien - Harmony
Ali Louis Bourzgi - Tommy
* the top four are pretty set for me (but only really the top two I think are REALLY guaranteed), could possibly see Brody Grant (Outsiders), Jeremy Jordan (Gatsby) or one of the Gutenberg boys here too
Best Actress in a Musical
Kelli O'Hara - Days of Wine and Roses
Maryann Plunkett - The Notebook
Shaina Taub - Suffs
Eden Espinosa - Lempicka
Maleah Joi Moon - Hell's Kitchen
* I could see Shaina Taub being dropped since she'll be nominated for book/score, or Eden Espinosa given that she's had a lot of vocal issues recently, but I think they'll both be acknowledged here. Gayle Rankin (Cabaret) was the main other wild card for me here, though I'd LOVE if Arielle Jacobs (Here Lies Love) got in
Best Featured Actor in a Musical
Daniel Radcliffe - Merrily We Roll Along
Steven Skybell - Cabaret
Ricky Ubeda - Illinoise
Paul Alexander Nolan - Water for Elephants
Conrad Ricamora - Here Lies Love
* If I'm being super honest, I think Ben Cook (Illinoise) probably has a better chance at the last slot, but I just needed something to believe in for Here Lies Love
Best Featured Actress in a Musical
Bebe Neuwirth - Cabaret
Lindsay Mendez - Merrily We Roll Along
Amber Iman - Lempicka
Jenn Colella - Suffs
Nikki M. James - Suffs
* The only ones I feel confident about are the top two, but I could also see this with Hanna Cruz (Suffs) and maybe Shoshana Bean (Hell's Kitchen). I honestly don't see Leslie Rodriguez Kritzer (Spamalot) getting a nom here, though I'd be quite happy for her if she did
Best Scenic Design in a Musical
Back to the Future
Here Lies Love
Cabaret
Gatsby
Water for Elephants
* I really don't see a world where the top 4 here don't get nominated, so I think the fifth slot is the one that's up for grabs, which I suppose could also be The Outsiders or Tommy (which I haven't seen) though people who saw the original production didn't seem to be impressed
I didn't really go into the play categories much because I haven't been following them as closely, but I wish all the best for Stereophonic and Jaja's African Hair Braiding in particular