Another site that offers discounts is playbill.com
You won't be able to find Billy Elliot discounts though. Most shows you can get discounts, but BE, Wicked, Lion King, and Jersey Boys are the show that never offer discounts.
Depending on how many people you have/if you live in or near the city, you can try to get lottery tickets or rush tickets. With the lottery, you go to the theatre 2.5 hours before curtain and enter your name into a lottery system to win $26ish tickets. 2 hours before curtain, they pull names. You can win 1 or 2 tickets. Where the tickets are depends on the show. Wicked, West Side Story, and In the Heights offer front-row seats, Hair has the box seats for lotto.
Some shows are easier to win, some are not. I won the In the Heights lotto the second time I played, but it took roughly 10ish times till I won the Wicked one. and I played WSS like 5 times and never won.
Also, there is rush tickets too. You have to check with the show, as some are general rush, and some are student rush (meaning only those with student IDs can get tickets). You go to the theatre around the time the box office opens (generally an hourish beforehand is good), and you get $25ish tickets randomly around the theatre. With rushing, they give out a certain number of tickets, so as long as you are within that number in line, you are guarenteed a ticket.
There is the TKTS booth, but it's still very expensive. 30-40% off of $120 is still waaaay too much for me.