Whats the nearest Amtrak station to Yellowstone National Park?

There are none anywhere near Yellowstone. The closest is Salt lake City, which has bus service to Bozeman (about 90 miles to the park). There’s also Havre and other towns along the Empire Builder route, but that’s in Northern Montana. The Amtrak buses go to Casper WY and Twin Falls ID, but that’s not near either. Greyhound goes to Bozeman.

Flying might be easier.