Train is often the easiest way to get to Aberystwyth, with a pretty two hour journey from Shrewsbury. I use the Network Rail website to figure times and cost.
- Off-peak train tickets from London (any train after 9:30am from Euston) cost £77 return.
- Off-peak from Birmingham International is £54.
For European visitors, or those changing planes in Amsterdam or Dubai, Birmingham International Airport is the easiest place to fly into, with a direct rail link. Manchester Airport is reasonable, but you will probably need to change trains twice. Train details and ticket purchase can be done here.
For USA visitors, you will probably need to travel via Heathrow (although there is a direct flight from Newark to Birmingham). Train from London would be via London Euston, changing in Birmingham. Drive from Heathrow takes 4.5 hours and I wouldn't do it the same day I arrived in Heathrow on an overnight flight.