Remi on 53rd and Osteria del Circo on 55th are both quite good (though not great) Italian restaurants with interesting decor very near where you're staying. If you order carefully, you should be able to meet your $50 max. My favorite Italian restaurant here is Babbo, which is downtown, hard to get a reservation at, and would cost more than that. But you might want to try Lupa, also downtown, another Batali restaurant which has very flavorful, rustic Italian food and would meet your budget.
I'm not much of a red meat eater, but in my view the best steakhouse by far in NYC is Peter Luger's in Brooklyn. It will cost more than $50 pp and they take only cash and house cards.