Not really a "day" out but a great place to go.
It's a cafe in a converted church in Cardiff which caters specifically for children under 8. Big play area with lots of lovely (mainly wooden) toys. Nice sofas, good coffees and food. Out of school hours they charge £1.50 per walking-8 yr old child for entry - unlimited time.
DS never wants to leave.
Website is www.cafejunior.com