Unfortunately, there’s no railway station left in Swaffham now serving the transport needs of the local population. Going back before the station was closed in 1968, there were services from Swaffham to King’s Lynn (via East Winch, Pentney & Bilney and Narborough & Pentley), from Swaffham to Dereham (via Scarning, Wendling, Fransham, Dunham and Sporle) which in turn connected to Norwich and Wymondham and from Swaffham to Thetford (via Holme Hale, Watton and Stow Bedon). It’s true that the Swaffham to Thetford line wasn’t that busy, but the line through from Norwich to King’s Lynn would have been enormously useful if it had been left open.
I’d never gone to look to see what remains at the site now, but the railway station is still there and converted into office use today. There are lots more photos of the station over the decades at http://www.disused-stations.org.uk/s/swaffham/.