The Disney shows don't sell tickets at the discount tkts booth. I've heard that you can go to the box office for the longer-running shows on the day of the show and sometimes get tickets (but I've never tried it).
For non-Disney musicals, I would try the tkts booth at the South Street Seaport. The lines are shorter there. You can look on line and see what they've had available in the last few days to get an idea of what might be possible.
https://www.tdf.org/nyc/7/TKTS-ticket-booths
FWIW, I usually buy tickets (from the theater or on StubHub, if necessary) for one show that I really want to see, and then take my chances with the TKTS booth for the rest of the trip. It's always worked out great.