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 Cold Knap (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
Google Earth aerial view of Barry with car parking indicated by the white arrow
Dogs banned between 1st May and 30th Sept