Howdy - -
You don't say where in Michigan - but I'm guessing somewhere along !-94 or I-96.
Baggage service on Amtrak is extremely limited - but is much cheaper than airlines.
$5 vs. $75 is a lont of change for some folks. They sell bike boxes at Amtrak stations - call first.
The Amtrak "boxes" are giant - - all you have to do is take off the pedals and turn the handlebars.
Plus - you have less hassle with all the gear you need for a bike tour.
You get checked baggage, as well as carry-on.
The good news - The Empire Builder - from Chicago to Seattle - is one of Amtrak's best trains.
It has the best ontime performance of any of the long-distance trains. Two-level cars. Diner and lounge.
The fair news - You Lakeshore Limited for NYC is an O.K. overnight train -
It's the only one with baggage service.
The bad news - There is no baggage service or bicycle roll-on on any Michigan train.
Thus you would have to drive to/from either Toledo or South Bend.
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If you could get someone to take you to Chicago and then catch the Empire Builder -
that would be the ideal Amtrak solution. There's a fast ferry from the Jersey Shore to Manhattan -
then you can catch the Lakeshore back to Toledo/South Bend from Grand Central Station.
The nice thing about taking the train out to Washington state is that it allows you time to decompress.
Same goes for taking the train back from the East coast. You usually have the chance to meet nice folks who are travelling for the fun of it - not a bunch of harried business people trying to make the next buck. You'll have the extra cost of meals - and you should really consider getting Mom or Grandma to front you something for meals on the train - because it's a pleasant break to eat in the diner.
If you have two days to take the train out West - I'd do it.