Train travel in the U.S. northeast

There is a train from the airport to 30th Street Station (Amtrak)

http://www.septa.com/service/sched/pdfs/R1Airport.pdf

You could also take a taxi. It isn't very far and the fee is a flat rate of $25, plus tip.

There are plenty of trains between Philadelphia and Boston, all going through NYC. At least two an hour. You will have the choice of a regular train, or an ACELA. ACELA is a little faster, makes fewer stops, and is more expensive. Both are all-reserved, which means you are guaranteed a seat, just not a specific seat. It's about a four hour train ride, I think.

At the Philly airport, there is a train stop just outside of the terminals B,C. The train goes into the city and I believe that it's every 30 or 40 minutes. This train would take you into the Amtrak station where you would then board a train to Boston. Alternatively, a taxi into the city to the train station would be around $35.

You can take the Acela or the regional train to Boston . Acela costs more and really does not save you very much time. The regional train would be around $140.00. The trip would be around 6 hours. If you are travelling during peak time, I would recommend a reservation.

There is just one Amtrak a day that goes due west from Boston towards Albany. It's the Lakeshore Limited, which goes all the way to Chicago. I took it once, a year ago, just the leg from Pittsfield MA to Boston, so I don't know where it stops in Albany. I believe it would be possible to get a rental car from Enterprise at one of the smaller stops, such as Pittsfield...Enterprise picks you up at the station and takes you to their office to get the car. This could save you driving in and out of the city. You could visit the Berkshires or Vermont easily from there. The train was remarkably cheap, I think it was just $10.

The other trains between Boston and Albany go down into New York City again, and back north, which takes along time. I'm pretty sure the only direct train is the Lakeshore.

although, in thinking about it a bit more, you might just want to rent a car in Boston. You can easily drive from there up into the White Mountains if its foliage you want to see. New Hampshire is much closer than the Adirondacks, and its a straight shot out of the city. No need to bother with schlepping your bags on another train. I do think you should consider making some accomodation reservations for foliage areas though. If you are thinking of Vermont or New Hampshire around Columbus day, things will be very booked up.

Agree that taking a train to Alban makes lieelt sense - since much of what you'll want to see is probably closer to Boston that early in the fall foliage season. No sense in sitting on a train for 6 hours, then renting a car and backtracking.

There is also one Amtrak train a day from Philly to St. Albans Vt you might want to consider instead of the route to Boston first, then Albany. (The Vermonter). I think foliage in the Adirondacks may be past peak by the time you were thinking of getting to that area.