It's playing at the American Repertory Theatre in Cambridge, MA. Previews are from August 2-August 19, and it's running for a little while after that as well.
Right now, if you have a multiple show subscription package, you can already get tickets for the preview nights, and it says remaining dates will go on sale July 3, and they start at $25.
ART has been updating the site a lot recently, and there's a picture of what I assume is a design for a set, and according to the hangout she did (and her Instagram), they started rehearsal last Tuesday!
The lead, Jenna, has been announced, and is Jessie Mueller, the person who won the tony last year for her portrayal of Carole King in Beautiful