Hello,
New York is an extremely busy and popular place in Budapest, especially in the summer and during weekends. It is only possible to book a table here from 18.00 in the evening. Between opening at 8:00 and 18:00, no reservations are possible and you enter at the order of arrival. In other words, you might have to stand in line if you arrive during a busy time. If you arrive at 8:00, you can most likely avoid the line, but later, it is very possible that you have to stand in line.
Reservations for the evenings can be done at https://newyorkcafe.hu/