I recently had a show published after being produced in the New York Musical Festival (NYMF). Publishers do attend shows there to scope out potential works to publish. However, I would not recommend NYMF unless you have someone with a lot of money to back your show, because it can get very expensive. I was lucky enough to have a producer who was willing to spend a large amount of money to make the production quality very high in order to attract publishers.

I would recommend putting on readings in NYC and inviting reps from publishing houses. Also create demos and send that along with your libretto to regional theatres which have an open submissions policy. There are numerous small theatres and festivals around the US that produce unpublished world premiere musicals and would offer a good opportunity for a starting production which could lead to other things. A few good ones off the top of my head:

Chicago: Underscore Theatre (my own company) Pride Films and Plays American Theatre Company Marriott Theatre Paramount Theatre Chicago Musical Theatre Festival (CMTF) FWD Theatre Project Chicago Theatre Workshop

NYC: Ars Nova New York Theatre Workshop Musical Theatre Factory New York Theatre Barn York Theatre

Check on Playbill.com periodically for other submission opportunities!