Welcome to the RoadTrip America forum!
I think that, on arriving in New York, you're really gonna be suffering with jetlag and, by the time you've cleared immigration, picked up your car and got on the highway, it's likely to be 3pm at best. I really don't see you covering 200-300 miles that afternoon. Especially after a 'quick look round ny'
If it were me I would probably be looking at a night or even two in NYC to find my feet before hitting the road. I'd probably take public transport into the city and pick the rental car up downtown as it is likely to be cheaper (and certainly easier) than picking it up at the airport. NYC is one place that I really wanna see sometime soon and, even though I've yet to visit, I know that seeing it in the space of a couple of hours is simply not going to happen.
What is the agenda for the rest of the trip? What plans do you currently have for the route? How many of you are there (be sure to take the Roadtrip Compatibility Quiz!) and what do you all want to see/do? What are you interests? Do you have any 'must-see' destinations and what are your reasons for them being 'must-see'?
You say you're all music fans, but what sort of music? There's the obvious destinations of Nashville, Memphis and New Orleans, is that your sort of thing? And, cool stuff for the snapper? There'll be no end of that, don't worry! See as many national parks as you can - you'll all love them and the snapper will be in heaven.