visit www.broadway.com this is a great resource for information on what is currently playing On Broadway and the notable and fantastic shows playing in the smaller Off-Broadway houses. (not a great site for tickets)
For full price tickets
Discount and day of tickets
www.broadwaybox.com up to 75% discount on select Broadway shows
The TKTS Booth at Father Duffy Square in Times Square. Click here to see what is currently on the boards at TKTS
Many of the best shows and theatircal events in New York are actually playing Off-Broadway. Here are some long running shows and institutions to check out.
The Blue Man Group - This is the theatre where it all started.