I visited Barry Island and Funfair every year when I was a child, Barry Island was invaded by the miners and their families from the Rhondda valleys ( I was from a miners family). Barry was an island a long time ago,but it is now joined to the mainland by a causeway.
The beach is flanked by a wide promenade where children can play in safety away from the traffic.
There is good car parking,(just follow the signs), with disabled parking spaces available on the seafront, a nice sandy beach for the kids,candy floss ,fair, and amusement arcades for the rainy days.
If you dont like sand in your shoes, or in the sandwiches, take a walk along Friar's Point, a grassy headland, which is to the right of the beach where there are benches to sit and relax.
Also worth a visit is (look out for the signs to the Knap) which is 1m West of Barry. This is a pebble beach with car parking, popular with older people like myself who prefers to sit in the car with a flask and sandwiches and watch the world go by.
Barry Island is easy to get to by car - just follow the tourist signs from Junction 33 of the M4 motorway