Some of the most historically and culturally rich sites to visit while in New York are:
Grand Central Terminal: An architectural and historic monument built in 1913 which has a number of shops and restaurants.
Museum of Modern Art: Though the name suggests modern art, this place boasts of artwork collection from the 1880's till date. There are plenty of good hotels but some of the best ones to stay in are- Hampton Inn Times Square North, Omni Berkshire Place, the New York Palace, Salisbury Hotel and New York Marriott Marquis etc.
Ground Zero Museum Workshop: A thoughtful and touching collection of images and artifacts from one of the most disastrous events in U.S. history.
New York Public Library: One of the most striking historic monuments in the city with the two stone lion statues as a special feature of this extensive source of information and knowledge.