TBH I have no idea what availability is like today, but (as an internet expert) I have some guesses.
Nine speed chains are probably more readily available than cassettes, especially if you want a particular size.
College towns are more likely to have either or both; thinking of Ashland, Charlottesville, Carbondale, Missoula. Tourist centers like Damascus, Canon City, and West Yellowstone probably have above-average chances.
Then there are the places in between. Off the top of my head I can't think of a place on the TransAm in Kentucky or Missouri that I'd bet would have the cassette you want, and your best shot at a chain might be Walmart.
You can plan for this, of course. Start with a new chain and cassette. Borrow a tape measure every week or so to track the chain wear. Be regular about wiping your chain clean, and re-lube it when it squeaks (like after a rain). You might carry a chain, buy one when it's looking iffy, or stop by a library or motel and order a chain to be delivered a week ahead of you (post office, General Delivery). You might order a fresh tire for the rear at the same time to see if you can get free shipping. Make sure your mini-tool includes a chain tool, and you can swap the chain when you need to, well before the cassette gets worn.