Gardens to visit in & around Cardiff

I'm off to Cardiff for a few days, mostly busy but I find myself with a spare day on Monday. I love walking around Cardiff, down to the bay etc., but fancy 'an outing'. Any suggestions?
I'll be using public transport, and Dewstow Gardens looks both interesting and doable, but I'm not sure if the walk at the other end is actually pedestrian-friendly: Google maps has had me skirting dual carriageways before!
Not a garden, but St Fagan's Museum also appeals. Or maybe Barry Island for the day.
What would you recommend?
I'll be using public transport, and Dewstow Gardens looks both interesting and doable, but I'm not sure if the walk at the other end is actually pedestrian-friendly: Google maps has had me skirting dual carriageways before!
Not a garden, but St Fagan's Museum also appeals. Or maybe Barry Island for the day.
What would you recommend?
'If you have a garden and a library, you have everything you need.'
- Cicero
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Tredegar also looks interesting.
It's something different.
It's years since l've been to Barry Island, but unless you're a big fan of Gavin and Stacey l'd probably go to a garden instead.
I'm going to see if I can find anything on YouTube about Dewstow. It'll be very frustrating if I then find that the walk from the station is impossible - it's only a mile but looks a bit hairy.
Really good to hear about St Fagans - I had it on my list based on having seen something about it ages ago, but I can't remember what!
I'm going to St Fagan's. The combination of good reviews, easy transport and it already being on my 'Places to go' list won me over. I'll go to Dewstow another time, perhaps when I'm not on my own.
So it's not really a gardening forum question any more (though the Airbnb where I'm staying advertises itself as having an amazing garden, so we shall see!).
Thanks all.
Enjoy St Fagans
But I'm going to stick to St Fagan's 🙂