California's Ocean Pacific Highway is also called Highway one by natives (or so I'm told) But which is it- Highway 1, Highway One, or Highway one? Oh, and while I'm asking is are the first letters in Ocean Pacific Highway all caps?
I've driven (and walked) on Highway One countless times. It says "1" on the highway signs, but they're highway signs--they get to abbreviate in ways that books, articles, stories etc. do not, because people have to be able to read them when flying down the highway at 60mph. Not that you'd ever drive that fast on most parts of Highway One, though (unless you're into driving off the sides of cliffs). I've never heard any locals refer to it as anything other than Highway One, although one particularly swoopy, curvy, difficult part of it is called Devil's Slide.
Anyway. Back to the topic.
If you spell it out, both words have to be capitalized because "Highway One" is a proper noun (it's the name of a specific highway). Not capitalizing both of them would be like any of the following: New york. Arnold schwarzenegger. Hip hop. All those are proper nouns--they're names of specific places, people or things. And all proper nouns are capitalized, which is why those examples look so wrong and weird.
Note, however, that certain words are always lowercase: Zorba
the Greek, for example. When trying to figure out how to capitalize a proper noun, refer to the rules on capitalization in titles: One Flew Over
the Cuckoo's Nest, etc.
*Edited to add* I would normally agree with the other poster that you shouldn't spell out highway names--I'd say Route 66, for example, or Interstate 79, etc. But I think those are left as digits instead of words just because spelling them out makes them so long. When you have a highway name as short as "Highway One," to me it feels more natural to spell it out.