Is there a way to rent a car from DC to NY?

You can do it, but it's not cheap. I tried a couple and didn't get a base rate lower than $150. So unless you're going to be gone for a month, this plan isn't going to save you any money.

All of the major car rentals will let you rent one way.

I fly out of JFK often, and I fly up from either Ronald Reagan National or BWI to make my connections.

This is my help from Washington, D.C. United States of America.

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Yes you can very well hire a car one way as this is the best option that you have as taking your own car won't be that good an idea. You can book a car at http://www.usacarsrental.com/ . The car they will provide you will be best in condition and that to at very cheap rate. You can hire the car from desired location and leave it to the best possible point you can. But do make sure to book the car in advance to avoid any hassles.

Any of them.