It would help if you would give us some specifics. What cuisines are preferred? What is the per person budget, and tell us if that figure includes alcoholic beverages, tax & tip?
Just to get you started...
Cibo, on the corner of 2nd Av. & 41st St., serves very good Tuscan/New American cuisine. In addition to the a la carte menu, they offer a 3-course lunch prix-fixe for $26.95. The large space has very attractive decor. No problem accommodating a group of 20.