With all that New York City has to offer, deciding which sites to visit in a three-day trip can be a daunting task. Your choices will vary depending on your personal interests, budget, time of year and the weather.lazas and Neighborhoods. Stroll around Times Square, site of the annual New Year's ball drop and frequent performances by pop stars. Stop by Rockefeller Center to visit the Radio City Music Hall, get a glimpse of the Today show, ice skate or shop.