As it's a skiing holiday, and I can't ski, I don't mind giving the answers ! First station is, I think, Amersham, from where he goes to Chalfont & Latimer then on to Chesham. This last leg is probably the longest distance between two Underground stations, hence the reference in the puzzle.
Amersham station most extreme on the Met line, and the highest station on the whole tube system.Braniac answered the Chesham one.
I dont ski either but would love to try,let fate decide.