We stayed in a couple this summer when my husband's leave was cancelled at short notice and I couldn't face camping with 3 children by myself .
If you go on the YHA website (and possibly tripadvisor too) you'll be able to see the reviews of individual hostels.
We stayed at one in Langdale in the Lakes and it was fabulous - just beautiful location, spotless kitchen, lovely lounge with games etc. We stayed in a family room (me, 2 x 7yr olds, 3 yr old) in bunks, was a fun adventure. We only used it as a base, we were out and about pretty much all day.
We stayed in a family ensuite room (not in Wales though) this year for the first time. The kids LOVED it. They liked having bunks, sleeping all in the same room, croissants, coco pops and hot choc from the brekkie buffet (we were on holiday). We were lucky enough to have the room opposite the quiet lounge so we could watch our door and sit outside the room. It was a fab location.
From an adult point of view some areas were quite skanky, although the communal kitchen was spotless. For us, it was only a few pounds cheaper than nearby cheap chain hotels and more basic.
I did as a kid and loved it, everyone else there was on different kinds of interesting holidays, the facilities can be fantastic and better than a hotel or very basic, but when they're basic it doesn't matter because the price means you're not disappointed
Don't know any in that area sorry OP, but just to say hostel-ing is a great way to have a holiday! My dc's are 9 & 12 and have enjoyed it a few times over the years. Only tip would be to book a family room if you can as my dd has been spooked (with no reason it seemd) before by a stranger in a dorm we once slept in. I also prefer a room with its own bathroom but then I like to pretend I'm actually in a hotel