Unfortunately, it is not feasible at this time...the Light Rail Train currently goes into downtown Minneapolis whereas the Amtrak station is in St. Paul (and, for that matter, not in downtown St. Paul). There is a planned second line that would go past the Amtrak station relatively closely, but that is at least years down the line (no pun intended). From the Amtrak station, you would need to take either a city bus to downtown Minneapolis or catch a cab. You can check out www.metrotransit.org for bus information, and it appears you would want the 50 line, which is a limited stop bus to downtown Minneapolis. I would guess a taxi to be about $15-20 to downtown Minneapolis.Edited: 7:43 pm, August 11, 2010
If you use the bus to get to downtown for light rail, it's on a fairly busy route so you wouldn't wait long for it.
However, I question whether the taxi would be that expensive. It's less than 4 miles to the Franklin Ave station (south of downtown), which appears to be the closest light rail stop. When I take a 4 mile cab ride from my office to home, it's around $12.
I might take my time and enjoy the sites getting to your hotel from the train. Then for expediency's sake, take a cab back when you're heading home.
If you do take the bus option to connect you with light rail, please know the buses and trains are operated by the same agency, metro transit. Which means if you buy a bus ticket to connect with light rail, you can use the same ticket to ride the train. Just so you don't think you need two separate tickets.
There is a thread on here from a week or so ago about a very similar thing, only getting to Amtrak from light rail. You can read up on that about which bus makes a good connection or use the route planner on metrotransit.org.
I'd estimate $15 to the light rail station, a smidge more if you have baggage.
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