If you rent a car in New York City, take the Verazanno Narrows Bridge to Staten Island and across it to New Jersey. If you are lucky and traffic is not heavy, you will be on the New Jersey Turnpike or Route 95 heading south within an hour. There are plenty of motels at most exits along either road. You can be in the outskirts of Philadelphia within three hours. You can be at Baltimore in five or Washington DC in seven hours. Take your pick, any place along the way, you can find good accommodations.
Most people driving to Florida from New York would drive to North or South Carolina in one day, then push on to Florida the next day. That is an agressive pace that requires about ten hours of driving each day, but allows you to arrive in Orlando within two days.
If you are in no hurry to get to Florida, you might want to stop in Philadelphia, Baltimore, Washington DC, Richmond, Myrtle Beach, Charleston, Savannah, or Saint Augustine. Each of them has some attractions to offer.