NYC weekend - College Budget Edition

My friend and I will be visiting NYC next weekend. We've both been to NYC - I used to live there - and would like to steer clear of tourist traps.

In addition we're now both unemployed, recent college grads; we're foodies (one of us is a vegetarian, but will eat meat on a "cultural experience basis") - we love ethnic food - but on a very tight budget.

We've combed through the obvious cheap eats columns, but a lot of them are all over the outer boroughs, and many are not even that cheap (we'd prefer most meals under $10pp, maybe one around $20 - yes we know, this is difficult). Can you chowhounds give us some recommendations?

We'll be staying in morningside heights, which we know is not a culinary wonderland by any means - obviously we'll be spending a lot of time downtown.

We also wanted to walk across the Brooklyn Bridge and get pizza. Grimaldi's is obviously an option, but we'd like something a little better that isn't a total shlep across Brooklyn. We thought about Lucali's but it's twice the price of Grimaldi's! Suggestions?

Thanks all!

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Grimaldi's
47 W 20th St, New York, NY 10010