There's a list of 24 hour Cardiff car parks here. (Scroll down for a contact form if you want to check for any length restrictions, height barriers etc)
Hi,
Which area of Cardiff will you want to be near?.
There are a couple of small campsites on the outskirts might let you leave it with them for a small fee.
We are babysitting in Splott. We managed to book at the Cardiff Caravan Park on the Friday night but the Steriophonics are holding a concert on the Saturday and the site is fully booked. In fact we just got the last space on the Friday and its not until June!!
I had asked Cardiff Campsite about Sophia gardens car park when i couldn't book the night I wanted and he said that he thought the council were tightening up on parking there.