I'm going to give you the answer you asked for but then I'm going to give you the answer you need. Ready for that? Okay, let's go.
If you really, really, really want to use your Apple TV in the car, what you need to be looking for is called a power inverter.You plug it into your cigarette lighter, and then just plug in with a normal plug. Cost should run you somewhere between $50 and $100, although I googled up this one for under $20. Make sure you buy one with a standard 110 plug socket. That's how we used to bring along our (full-sized!) VCR. There are, however, a whole bunch of problems with you plan that you need to know about.
First of all, power inverters tend to be noisy. That's because they use a fan to keep themselves cool. Some higher-end units use noise filters, making them less obnoxious but at a rather higher price. Also, they generally don't work with uninterupted power supplies (UPS), and there's simply no clean way to power down your Apple TV, and every time you shut off your motor, the power will go away.
Second, the last time I checked, Apple TV doesn't do composite output; only component and HDMI. A quick google reveals that converters (often requiring their own power source) hover between $100 to $200.
Third, you need to carry along another set of cables, since it's unlikely that your rental accommodations will supply cables for you and may end up needing to use your component-to-composite converter at your lodgings.
And there's more. The Apple TV uses a built-in hard drive. Not flash memory. That means that it's not going to be happy when your car goes bumpy bumpy bumpy along some less than driver friendly roads. You may permanently destroy your little Apple TV friend.
Oh, and did I mention that the Apple TV alone gets hot enough to (almost) fry eggs? So be prepared to give it a lot of air ventilation, while somehow keeping it steady on the road.
With all that said, there's really a much simpler solution. Buy or borrow an iPod touch. (An iPhone, of course, would be even better -- because you can use it with 3G data service along the road.) An iPod provides all the same movie playback features of an Apple TV, syncs data just like an Apple TV, plus is fully compatible with the standard $50 Apple Composite Video-Out-Cable, that includes a USB-power dongle. To use, connect the dongle to a cheap (usually under $20) cigarette-lighter to USB adapter for clean 5V power, and you can use your car's built-in power and video systems.
When you arrive at your destination, you can use the same cable to watch on your (typically composite) TV. (If things are really dire, use an RF Modulator for TVs with coax-in only. And if you only have antenna-in? Hit up your local Radio Shack and throw yourself on their mercy. I still have one coax-to-antenna converter on hand but, thankfully, haven't needed to use it in years.)
Of course, if things are good (and by good, I mean a relatively modern TV and in-room Wi-Fi), then with an iPod touch, you also have the option of renting movies on the go, so you don't have to spend a ton of time preparing your device at home. Which is kind of great, as you get to be a lot more spontaneous.
Plus, you can do that thing where you stick earphones into your iPod and listen to that stuff called "Music", while the iPod rides along in your hip pocket. It's a little hard to do that with an Apple TV.
Love and Hugs,