re: NYC Restaurant for little girl’s birthday?

I’ll offer another suggestion: the American Girl cafe. If she has one of their dolls, bring it with you, as they have special chairs for the dolls to sit at the table. Just walking thru the store to reach the cafe will be fun, though you may end up leaving with more than you planned for! My daughters and I have wonderful memories from dining at the American Girl cafes when they were around the age of your daughter.