I've never stayed at a hostel, but a cheap (and from what I hear, safer) place to stay is the YMCA West Side. It's located a block away from Columbus Circle so it is walking distance to Broadway theaters (20 blocks) or take the A/C train for a quick drop-off. The YMCA West Side are private rooms but community bathrooms. Some rooms have private baths. Some rooms have bunkbeds, others have double beds, but the standard is a single full size bed. They are very basic with bed, TV, desk, closet, lamp.
For tickets to shows, student rush/general rush/lottery/TDF/TKTS.
For food, fast food is your best bet BUT some other sit-down places and delis can be just as cheap for better food. The YMCA West Side also has a little eatery downstairs.
"The Spectacle has, indeed, an emotional attraction of its own, but, of all the parts, it is the least artistic, and connected least with the art of poetry. For the power of Tragedy, we may be sure, is felt even apart from representation and actors. Besides, the production of spectacular effects depends more on the art of the stage machinist than on that of the poet."
--Aristotle
