Another vote for the Cardiff Caravan Site here. It's a municipal site, Very helpful and friendly reception; decent sized pitches; dated but usable facilities block. It's right on Bute Park so a lovely walk into the centre. From Bute Park you can also get a river ferry down to the Bay area. Also the Park is on the cycle route up to Castell Coch too. It's a shorter walk to Cathedral road which is a local centre with shops, resto's etc
For anyone searching on this thread in the future, a couple of things about the site though: it gets booked up very early if there is an event on at the Principality Stadium so book early. Also we found that the site was in a wifi/mobile phone blackspot for EE coverage. There is free wifi at reception which works well but not on the rest of the site.
The cycle hire place (they gave a café too from memory) is a really thriving business. They seem to do a fair deal of outreach stuff too and have a number of dual bikes for folks who would struggle on their own.