I need some help with my itinerary and travel plans!
From London, I want to take a train to Bath early morning. Now, I am also dying to see the Tintern Abby and Caerphilly.
How long should I plan to stay and sight see in Bath?
I was thinking maybe from Bath, traveling to Cardiff afterwards, sleep there and explore the area the following day.
But I am also concerned about getting from Cardiff to the sights. Is it better to rent a car? (We are from the US) or is there a bus/train system that would work best? Taxi? I don't like the limited options of the tours I found.
Bath to Cardiff and Cardiff to Caerphilly can be done by train.
There's a bus, I think, from Cardiff to Tintern, but the abbey is about a mile south of the village. For most of this segment you'd retrace the track from the Severn Crossing all the way in to Cardiff before roughly paralleling the Wye. I don't know if you could break the bus trip at the neat little village of Chepstow with another excellent small castle.
It'd be really easy with a car from Bath.
Bath to Cardiff is quite easy by train - takes 1 hour and the trains are hourly. I don't think it is any cheaper by booking ahead so you might as well pay on the day. Trains can get crowded at commuting times Monday to Friday.
It is an easy 20 minute train ride from Cardiff Central or Queen Street to Caerphilly with trains roughly every 15 minutes (less on Sundays). Caerphilly Castle is a very impressive medieval fortress but the town is rather tatty = former coal mining area. It is only about 6 minute walk down the main street from the station to the castle.
Cardiff Castle is found right in the centre of the city and spans many historical periods. About 4th September, 2014 Barack Obama & other world leaders will be visiting Cardiff Castle for a banquet as part of a NATO conference so hotel prices will be high and the castle closed to the general public.
To reach Tintern from Cardiff, it is best to take a train to Chepstow and then a local bus to Tintern. The buses are every other hour so it is rather inconvenient. Put in for journey here > http://www.traveline-cymru.info The bus should stop near the ruined Abbey. If going from Bath to Tintern, you would need to change at Severn Tunnel Junction or Newport. Go to www.nationalrail.co.uk insert the journey and follow the instructions.
http://cadw.wales.gov.uk/daysout/tinternabbey/?lang=en
http://www.seewales.com do Day tours from Cardiff.
You can find out more about Cardiff from a previous post. (You can't do it all in 1 day).
https://community.ricksteves.com/travel-forum/england/day-trip-to-cardiff-bay
In reading your post are you thinking of more or less stopping by Bath on the way to Cardiff? If so, it really depends on what your interests are. You could probably do the Roman Baths (2-3 hours if you don't linger) and if you time it right pick up a walking tour around the central area and get some highlights in total of 6 or 7 hours.
Many people do Bath as a day trip from London, but I really enjoyed staying there 3 nights. I found a lot to do in Bath and just loved the juxtaposition of the Roman Bath and the Georgian Bath.