Just been to cardiff and had a fab time. not sure if you can do it in budget but we stayed within walking distance of the town centre and enjoyed the castle and the white water centre. lots of great shops and places to eat and the bayside is fab.
What about North Devon? Places like cottages4you do cheap apartments on the coast. We stayed at a really cute apartment called seagulls loft in ilfracombe for peanuts last year. Amazing beaches, dramatic coastal walks, art places, cosy pubs. Not posh but perfect break. If you get a sunny day it's paradise but we found lots to do in the rain too. Oh and there were loads of books/DVDs in the apartment too.