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.
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.
Have booked a super cultural lovely holiday for the summer with DP- but this has kind of sucked up all of our savings. Naice holiday isn't until July, but we're both really itching to just jump on a train and going somewhere late May or early June.
I know we're not guaranteed sun that time of year- but a part of the UK where there's a good chance of it helps, open to cheap hotel, chalet camping, whatever- we just want to escape for a few days with some carrier bags full of booze and live off fish and chips and pub food, only emerging to go for a night out of a nice long walk.
Don't want to spend more that £200 on train tickets and accommodation, and are looking to stay Thursday night to Sunday morning.