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If you aren't fussed what you see then I'd wait and buy when you got there.
Google TKTS booth. It's on Times Square and they sell tickets for shows same day at reduced rates. If you look online you can get an idea of the sort of shows that they have available. It won't be the most popular ones (i.e. not Hamilton) but plenty of good ones. My memory of Broadway was that the tickets were really, really expensive so getting them with some money off was a definite bonus.
Is it best to book online now, for August this year? Or wait and book when we get there?
Not too fussed about what we go to see, just keen to see something.