Machynlleth is a ~2 hour drive from Birmingham, a ~4 hour drive from London, a ~2.5 hour drive from Cardiff and a ~2 hour drive from Liverpool. All traffic dependant of course!
Bwlch y Groes Faen is a 5 minute drive from the town centre. Further more detailed directions will be provided upon booking.
Machynlleth has a well serviced train station with direct trains to and from Shrewsbury (1 hour 15 minutes) and Birmingham (2.5 hours). From London Euston, the journey takes ~4 hours (changing at either Birmingham or Shrewsbury).