At this point, for high-profile shows, you are better off doing Rush or Lotto (or Standing Room, if offered).
If not, and you can afford full-price ticket prices, I have a suggestion:
Seats are often put off-sale to hold for emergencies and/or premium tickets. If they don't get sold, then they are released. "Holds" and "Premiums" are now available at full-price. Holds are typically released 2 days prior to showtime, and Emergencies about 2 hours prior to showtime. Just go to the box office and try your luck.
Otherwise:
Try your luck at the TKTS line. Those are discount tickets, but the high-profile shows sell-out fast. And just because a show is not listed on there when the TKTS booth opens doesn't mean it won't appear later in the day. Try an hour before showtime.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle
