I think Hamilton will sweep book, score, musical, direction (I think Arden deserves it, but it will be closed: Out of sight, out of mind), choreography, lighting, set, costume, orchestrations, and actor (Leslie Odom, Jr.-he belongs in leading and I think he's going to win. IMO, he's giving the best performance there.)
There are two other awards it COULD get I think, but the categories might be tougher:
Featured Actor: Daveed Diggs
Featured Actress: Renee Elise Goldsberry
The thing with featured actress is that there will be ladies from The Color Purple in there (Jennifer Hudson is probably big competition). There will also be Jane Krakowski from She Loves Me. That category is by no means a cake walk for Goldsberry (who won't be eligible for any pre-Tony awards this season).
Featured Actor has George Takei plus there could be other Hamilton nominees there.
I suspect Odom will take it and think Diggs and Goldsberry are in the running.