Going to the seaside and going to the sea
Solution 1:
There are reasons why Americans talk about going to the beach, or the Australians to the sea, whereas Europeans talk of the seaside (French 'bord de la mer', meaning seaside).
It has to do with the development of 'seaside holidays' in England and France in the late nineteenth century, facilitated by the arrival of railways. European resorts emerged based on a town with promenade, shops, hotels, theatres etc close by. Many became highly fashionable, not only in the south of France, but some resorts in Britain too. Brighton is renowned for its Royal Pavillion, built in the reign of George IV, much earlier in the century, but such places as Cromer on the north Norfolk coast, Bognor Regis, Bournemouth etc were highly fashionable resorts by Edwardian times. These sorts of places, together with many others constitute 'seaside resorts'.
In America the tradition of going to the 'beach' grew up in a slightly different way. American beaches, in days when people began using them recreationally, were simply that, i.e. 'beaches', with no town for miles. This is still, to some extent, the case in the massive, underpopulated land of Australia, When Aussies go to the sea, it often means just that.