From Syracuse, NY to Fayetteville, NC. I would stay at Hampton Inn and Suites Fayetteville, NC. From Syracuse to Frederick, Maryland would be my 5 hour stop. These conditions are variable due to weather and traffic. From Fayetteville,NC to Jacksonville, Florida is close to 5 hours. I would stop South of Jacksonville. Enjoy your trip. It's a long drive. 500 miles = 8 hours. From Syracuse to Miami is about 1500 miles. Best wishes for a safe trip. 1 case of water per person/pet.