To get to Chepstow by car, follow the M4 until Junction 21, then take the M48 and exit at Junction 2 onto the A466. Follow the signs to Chepstow. From Bristol, take the M32 and then the M4, and follow the same directions. From Cardiff, take the A48 and then the M48, exiting at Junction 2 onto the A466.
If you prefer to take public transport, Chepstow has both a train station and a bus station. From Bristol, take a direct train from Bristol Temple Meads station. From Cardiff, take a train from Cardiff Central station. Buses run regularly from both cities as well.
If you're already in Monmouthshire, why not take a scenic drive along the Wye Valley? From Monmouth, follow the A466 south and enjoy the beautiful views along the way.
The closest airport to Chepstow is Bristol Airport. It is approximately 17 miles away and can be reached by taking the M48 and then the M5. Alternatively, there is also Cardiff Airport which is approximately 30 miles away and can be reached by taking the M4.