I agree with you on Broadwaybox.com. The original poster is likely not familiar with te discont theater scene for Broadway, so let me elaborate a bit:
First, you can find the latest show listings at Playbill.com. One of he features on this site is Broadway Groses where they list how well the various shows did in the last two weeks. Generally those above 90% are not available at a discount (the one exception is TKTS, which I will discss below). Newer shows (such as the upcoming "Violet", "Rocky" or "If/Then" are looking for advance bookings and are often available at a discount (that's where BroadwayBox.com comes in). Basically, BroadwayBox links yuou to the regualr ticket (Telecharge or Tickmaster) website and provides a discount code.
TKTS is a stand in Times Square that sells last minute tickets at deep discount (used to be 50%) for shows that day. Even the most popular shows will show up here late in the day. These are the tickets that the theater has not sold. At times you can get really great seats there as theaters generalluy hold their best )"house" seats till around 5 and then send them over to TKTS. BUT if you really want to see a specific show, the odds probably are not in your favor. Besides, the lines there can be long, and by the time you get to the window the pickings can be slim.
My wife and I generally go to NYC yearly and do a show intensive weekend (with planning, you can do 5 shows on a weekend}. We are going this May and want to see "Book of Morman", "Kinky Boots" and "Pippin". These are all popular shows and discounts are generally not available - so we booked those tickets directly through ticket master. The other two shows will be fdiscount shows (likely "Violet" and "IF/Then")those we will buy later. For the popular shows we bought the tickets early in order to get the best seats (you get to pick the seats that you want} (we decided when we wanted to go based on when we could get decent seats to "The Book of Morman").
Enjoy the show! :)