The closest train stations are Aberystwyth or Carmarthen. From there you will have to grab a taxi (around 50 minutes) or take the bus to Aberaeron.
3 hours from Birmingham via the A44. 2 hours from Cardiff via the M4 or 3 and a half hours from Liverpool via the A483. Generally, it’s advised to head to Aberystwyth and follow the coastal road from there.