You would travel 52 hours on the California Zephyr to Chicago and from there you’d take the Lake Shore Limited line for another 20 hours. A total of 3,397 miles (5,467 km) for only $193!
To book this, you have to search for the Emeryville, CA to New York – Penn Station route at Amtrak. Both trains travel on a daily schedule:
You need a credit card for the booking, but that’s something that you need to have anyways if you’re going to travel to the USA.
Obviously you won’t be sitting in the comfortable Roomette for that price, but the trains are somewhat more comfortable than many European trains.
It is not the goal to get from A to B, but to enjoy the landscape along the way. The California Zephyr, for instance, crosses the Rocky Mountains and the Sierra Nevada on its 2,438-mile (3,924 km) route.
If you don’t want to spend 69 (almost consecutive) hours on a train can also break down the trip into smaller segments and visit the cities and national parks on the way. The California Zephyr stops in Sacramento (California), Salt Lake City (Utah), Denver (Colorado), and Omaha (Nebraska), among others. The Lake Shore Limited line also offers the opportunity to explore Cleveland (Ohio) or Pittsfield (Massachusetts).
To do the trip with stops along the way, you should get a Rail Pass:
USA Rail Pass: $459 for 15 Days
With Amtrak’s Rail Pass, you can, for instance, travel anywhere in the USA for 15 days for US$459 (~€431) using up to 8 segments.
A segment begins with you boarding a train, bus, or ferry, and ends once you deboard.