One day in Cardiff, Wales with a kid

You might be better posting in the Wales forum. Also might be worth noting the schools break up for summer on July 20th in general so your experience might be different depending when you are there.
So Fagans is good but it does involve quite a lot of walking but you can pay yourself and there is a playground and lovely gardens to relax in too. You might have to swing by the bakery or w
Sweet shop but it's all part of the experience (these are located in the original buildings). To get there you will need to take a bus which is no more than 15/20 minutes and which you can catch relatively easily from the train station.
Other options include Cardiff Castle, check out their programme as they often run additional activities during the summer like jousting and falconry. It's about 10 minute walk for a 5 year old. From there you could move on to the National museum which has some interactive exhibits) or you could go to Cardiff Bay, perhaps catch the river boat down. During the holidays there is a large funfair. You can also visit teqniquest which a 5 year old would definitely enjoy (hands on science) and there's a great sandy play area if you walk down to the barrage (I thin it's part way along) just head for the little white wooden church and keep going.
I'd definitely recommend. If you're in Bath you may get also like a day trip to Bristol. It's a bit more spread out in terms of attractions but the SS Great Britain is fun and there is also a science type place @Bistol with an aquarium (small) next door.

Oh and you won't have any problem finding lunch or sweet treats. Cardiff city centre and Cardif bay have multiple options. At St Fagans there is a Cafe but another option would be to go out of the gates at the Castle/gardens side and over the road is a nice pub called the Plymouth Arms. As mentioned above, there are some nice treat options within the St Fagans buildings close to the Gwalia stores. Buy freshly baked bread or scones and fudge is always my treat. There all also plenty of ice cream carts.

ryan and gill offer sound advice. You will need Easyway bus 32A to reach St.Fagans Museum /Castle. The timetable is here:> https://museum.wales/media/34378/32A-Timetable-March2015.pdf
https://museum.wales/stfagans/

You will need to walk for about 9 minutes from the Central Station to Westgate Street (northbound) & find bus stop ‘KN’.
This is a good site for finding bus routes in Wales:> http://www.traveline-cymru.info

(Much redevelopment work is going on north of Cardiff Central Station).

On return to the city centre, I would get off at the *first stop after crossing the river = Westgate Street southbound. After crossing the river, on your left you will see Bute Park & Cardiff Castle. Consider visiting these after having seen St. Fagans. Then wander through the city centre back to the Central Station. (Or take a number 6 bus to Cardiff Bay from Westgate Street (southbound) - exact money only on this bus - no change given). On return from the Bay, get off bus 6 on the south side of the Central Station for train back to Bath. * If you want to go straight to the Central Station, the last (southernmost) stop in Westgate Street is the one to alight from the 32A.
https://www.cardiffcastle.com
http://www.mermaidquay.co.uk
http://www.visitcardiff.com

Thank you! These details on which buses to take are so helpful--I think my biggest concern for this trip is getting to and from places and not getting stuck somewhere unfamiliar with my child in tow.

Be sure to put your hand out when you see the Easyway bus 32A coming up Westgate Street - or it might not stop at the bus stop. There will be many buses passing but this bus will be small and white. (Google Easyway bus images).