If you look at my overall map, within a little over 100 miles of DC: http://mgrunes.com/dcicerinksmap.html
you will see where many rinks are, from Richmond, VA, through MD, DE, to Aston, PA. (BTW, Aston looks like a really nice skating complex, based on my one short visit. I think they have 4 indoor ice surfaces, so probably have a lot of ice time.)
If you click on the broken box icon near the upper right, you will get a bigger map. This is a Google map, so you can You can use "+" and "-", near the lower left, to zoom in and out, and you can drag the map around to pan it. Click on a red "+" to find out which rink is chosen.
Like I mentioned, traffic on 95 near Richmond can be pretty heavy, and take several extra hours, too. They have their own Beltway, which goes a little faster. Near Richmond, DC, never go inside the Beltway. Stay outside Philadelphia to the extent you can too. If you drive in the heaviest traffic times, you may even want to use 295 to skip most of 95 near Philadelphia. Locals know the (relatively) fast routes, you don't.
When I drove from Maryland (near DC) to Florida and back, I had to be careful of alligators at rest stops by the time I got to the Carolinas. But I guess you know all about that. (If I lived in Florida, I would probably never have gotten into hiking and camping.) I originally booked a hotel midway, but the 12-14 hours I lost in traffic jams made me change my mind, because I missed my hotel reservation (good thing I had a cell phone). I slept for 2 hours at a time at rest stops, and maybe camped once along the way. Of course, I like roughing it a bit - maybe you like hotels.
I get what you say about needing a car long-term. But you might be surprised how little most NYC residents use cars to get around NYC. Some of my relatives there don't have a car at all, or pay hundreds of dollars or more per month to park, a long ways from where they live. But I don't live there - other people should advise whether you need one at all, beyond an occasional taxi. Probably depends on where you need to go. Don't leave valuables visible in a car - I knew a traveler who lost everything. And always lock your car, though it may sometimes be opened anyway. (As it would be, if you parked much in downtown DC, or Baltimore.)