We went from Fort Worth, Texas overnight to Chicago... we missed our connecting train because our train was late and Amtrak paid for our hotel for the night. We then took another overnight to Pittsburg, switched trains there and went to Philadelphia. Of course we were a day behind and our first night at Philadelphia wasn't refundable.
If there is no public transportation at your destinations, you will most likely need a car. While in Philadelphia, we thought we'd walk from the station to the hotel... it didn't LOOK far on the map.
From that point, we went on an Adventures by Disney tour of Philadelphia, Washington, D.C., and Colonial Williamsburg.
We took a cab from our hotel to the trainstation in Williamsburg... a train to D.C., another train to Pittsburg, another to Chicago, and another home.
By the end of the trip, we never wanted to see a train again. And we could feel the "rocking" of the train for a couple of days after the trip was older.
Good points about the train:
1. The seats are larger and further apart than airplane coach... more like airplane first class.
2. Some trains had power outlets at the seats.
3. You can get up and walk around.
4. The observation car is pretty cool.
Bad points about the train:
1. Schedule? Hahahahaha! We started late and never caught up... it was a bad year for flooding (like this year) and there was extra freight train traffic. Freight trains have priority over passenger trains.
2. Overnight trains... unless you are willing to shell out big bucks for a private "room", you'll be sleeping with LOTS of other people around you. And there isn't that much room on the seat when you're trying to sleep in a reclining train chair... right next to someone (my grown daughter in this case). And while there is a light's out/quiet time, people are people and they make noises all night.
3. You don't always get to spread out... they put is in cars, based on our destination. Several times we were packed in, with no extra room... while other cars were practically (or sometimes totally) empty. If you try to switch seats you might "get in trouble"... we had moved because of a very large and annoying family behind us. We had to move back...

4. Food... unless you bring your own food, be prepared to pay too much for mediocre food. Dining car was "okay"... snack car was "okay"... but a couple of days of that is too much.
If I could take a "day trip" on a train, I probably would. The commuter trains we were on were pretty nice. Overnight... probably not. Not even with a private sleeper because the price isn't "worth it" to me.