There's an ibis in the centre that's reasonable but parking may not be.
I love, love love Cardiff. I visit 4 times a year. I'm English by birth, Irish and Scottish by descent and welsh by adoption. The only reason we have a welsh arm inthe family is because my great aunt had the good fortune to marry a Welshman so had lots of lovely holidays there as a child.
We stay out by Barry now as that is where the family is settled. We like to drive up the valleys as. We love the scenery. The big pit at blaenavon is free and a must do . Also there are some caves inthe brecon beacons. They had closed by the time wegotthere but enjoyed the standing stones outside, the very odd looking sheep and the llamas.
If you are down the bay have a quick look at the norwegian church. Roald Dahl was from Cardiff .
Shopping is great in the centre . Lots of lovely little arcades to poke around as well as the market and all the new modern stuff. The Cardiff story in the centre is free and you can always at eat at red hot which is superb . Its a buffet that is beautifully presented or if you you are down the bay there is Cosmo another buffet again which is very nicely done. Lat time we were in wagamamas inthe bay Charlotte church was in there with her kids and fiancé.
Cosmeston lakes down by Sully and Lavernock is lovely. They also have some old buildings you can mooch around but it's not on the scale of st Fagans . Don't forget Cardiff museum is very good and also free.
Barry island where Gavin and Stacey was filmed is also great on a nice day.
There's so much free stuff to do down there I'd be inclined todo that first and get a good feel for the place and then plan a later trip if you really want to see the dr who exhibition.
Have you read the trip advisor reviews. They seem very mixed ( my grandson is a big fan) and it sounded very expensive for a family.
I'm not back till august. I fell in love with the place when I was 8 andmy ten year old grandson has as well.