A bunch of things for you, Bill,

First, the best way to get discount tickets is:Broadway Box --it's a community site that gives you the producer's discount codes, which you can use to buy tickets on-line,by phone, or from the theatre box office.

And yes, the Tony's are restricted to shows at "Broadway"theatres, which are a determined by the size of the theatre--The Broadway theatres must have Equity and craft contracts, must pay scale based on the size of the theatre, and must maintain an orchestra of a certain size--

Off-Broadway shows receive Obie Awards--and off-Broadway theatres are smaller and have Equity and craft scales that are lower than the Broadway houses--off Broadway is regarded by many as the real "serious" theater of New York--Then there is Off-Off Broadway, and even shows that are presented in converted apartments--still something for everyone--

Oh, and Broadway Box has shows outside of New York,as well--even London shows!