Poughkeepsie, NY
Spokane, Washington is the closest Amtrak station to Hamilton, MT. From Spokane you can go west to Portland or Seattle or east to St. Paul/Minneapolis or Chicago on the Empire Builder.
West Glacier - Amtrak station - was created in 1910.
The closest Amtrak station to Missoula is in Whitefish, Montana, about 135 miles to the north (about 2½ hours by car). Rimrock Stages provides bus service between Missoula and Whitefish once a day, but the connections to Amtrak aren't very good.
Harpers Ferry, WV. From there you can go east to Washington DC or west to Pittsburgh or Chicago.
Alliance, Ohio where you can catch the Capitol Limited east to Pittsburgh and Washington, DC or west to Chicago.
Although Granby is physically the closest station to Loveland, Denver is probably the best year-round choice. From Denver, you can take the California Zephyr east to Chicago or west to San Francisco.
Las Vegas, NM, where you can take the Southwest Chief north to Chicago or west to Albuquerque or Los Angeles.
Needles, CA. From there, you can take the Southwest Chief east to Albuquerque and Chicago or west to Los Angeles.
Las Vegas, NM. From there, you can take the Southwest Chief north to Chicago or west to Albuquerque or Los Angeles.
Erie, PA. From there you can take the Lake Shore Limited east to Albany, Boston or New York or west to Chicago.
Prince, WV. From there you can take the Cardinal east to Washington, DC and New York City or west to Cincinnati, Indianapolis and Chicago.
Amtrak and Septa share a station at Trenton, NJ. There is another Septa Station at West Trenton NJ (Septa R-3 line) which is not served by Amtrak.