The United Nations building is located on the far eastern end of New York’s mid-town district. It sits at First Avenue between 42nd to 48th streets. Nearby hotels on the east side of town are plentiful and you should consider booking one within walking distance of the UN. On the matter of booking a hotel room(s), it is important to do so as far in advance as possible.
There are also websites for short-term apartments that can accommodate differing numbers of people. Prices for hotels and apartments can range from moderate to very expensive. Research your options well in advance.