When visiting New York City, its worthwhile to get acquainted with the lifestyle of New Yorkers. The city that never sleeps is always full of busy people walking fast, very fast, so keep up to speed or prepare to be yelled at.
Familiarize yourself with the subway system, that will probably be your best way to move around.
New York is always busy, avoid peak hours during the weekdays. Weekends are more relaxed.
Summer is always a good time to visit. Avoid going during Christmas time. New York is normally crowded, around the holidays it is nearly impossible to walk.
If you know someone in New York, ask if you can stay with them. That would save a hotel stay. Another option is using Airbnb. The best way to explore the city is using public transportation, the metro to be exact.