Chepstow is in the Welsh borderlands in south east Monmouthshire, easy to reach by road, rail or coach.

Cadw provide their own advice for getting to the castle here: https://cadw.gov.wales/visit/places-to-visit/chepstow-castle

If you come by public transport, Chepstow Castle is typically around a 10 minute walk from wherever you land your dragon / tie up your kraken / park the TARDIS

Chepstow is more or less one long hill down to the riverside, so expect to be walking up or down hill during your visit.

By Train

Chepstow Station is on a direct route to destinations such as Birmingham New Street in the Midlands, London Paddington (typically changing at Newport South Wales) in the South East of England and Exeter St Davids (typically changing at Newport, South Wales) in the South West of England.  And if you're in Wales typically the connecting station is Newport.

https://www.nationalrail.co.uk/stations/chepstow/

You'll pass the local Tescos on your way into town, so if you need a pit stop that's one option for you.

By Coach

There is a National Express coach stop in Chepstow on a direct east-west route.  That includes a direct route to Swansea and London Victoria.  North-South you may need to split your journey either changing in Cardiff if you want to stay on coaches (a bit of a round about route) or potentially switching to train in Newport South Wales, or Bristol.

https://www.nationalexpress.com/en

The bus stop is by the local M&S Foodhall (this is not just any National Express bus stop...) and you are right at the top of the high street so once you pass through the town gate you'll be passing pretty much every shop in town on your way down to the castle.

By Car

If you are staying overnight you might want to simply walk to the castle from your accomodation.

If you are there an back in the day or wish to park by the venue, the Castle has a large pay and display car park. At time of writing (15.11.2023) all day parking is £4.40. 

There are EV charging points there, but if you drive an electric car you know to check availability before you rely too heavily on any one EV point.  There are plenty of others around town (I warn you, the one by the library is pants). The fastest is at the Two Rivers restaurant (50kw), which is unhelpfully at the other end of town.  But if you have an electric vehicle I'm sure you're used to playing the 'where do I recharge' game.