Oooh! I have one the same age! (But a boy.)
Most of the stuff I know is London-based, but some of the info is transferable.
For instance: I'm taking him to Brian and Robin's Christmas Compendium in December at the Apollo in Hammersmith - hosted by Brian Cox and Robin Ince, it's a nerd xmas show, a sort of science cabaret with a ton of acts. I've taken him every year for the last two years, and it's quite expensive, but worth it. They have rather surprising guests - last year the musical turn was, er, the Cure, and the year before it was Canadian Astronaut Chris Hadfield. Most top-price tickets are gone but it's a huge venue so still some cheaper tickets left: www.eventimapollo.com/events/detail/brian-and-robins-christmas-compendium-of-reason-2
There's Ada Lovelace Day coming up, a "celebration of women and girls in science" - there's another science cabaret in London on the 13th Oct as part of this, one with all women on the stage, but it's a schoolnight I imagine, so no good for you. However, there's also lots of local events celebrating women and girls in STEM, so there might be one you fancy on their map here: findingada.com/worldwide-events/
(This map is zoomable so you can go in and see if there's anything you fancy. I can't see anything in Wales at the mo, but there's stuff being added all the time so check back.)
Still on the subject of shows, there's an act called "Festival of the Spoken Nerd" (@FOTSN) who are very funny - their shows are 14 and over (an occasional swear, I think, plus tinies wouldn't find it interesting) but as soon as DS hits 14 I am taking him. They are doing a tour, here, inc shows in Cardiff, Aberystwyth and Bath: festivalofthespokennerd.com/buy-tickets/
I don't know if you are on twitter, but if you are, and you follow things like @FOTSN, then you will get to find out other accounts that list nerdy fun science things. There are all kinds of smaller shows (smaller than FOTSN, I mean) and events all over the place, many of them free or very reasonably-priced.
Also, see if Cardiff or Bristol Universities have public engagement programmes - Imperial College here, which is obviously one of the top engineering/sci places, has all kinds of festivals and events over the course of the year, including weekend-long ones which have all kinds of child and teen-friendly (and free) activities - we've had some fantastic times there. It's possible other universities have the same, if only you can get on their mailing lists. Follow @ImperialSpark on twitter.
There's more - will come back here as I think of stuff but that's it for the moment.