San Sebastian. A bit pricey but so worth it and great for a solo traveller. You will love the place, the Concha (beach area) and especially bar/pintxo hopping in the Old Town. So charming, so vibrant, so friendly, so nice. Easy bus transfer from Bilbao.
Nice/Antibes/Menton, again gorgeous spots with everything you could want. Beach in Nice is stones, but there are lovely sandy beaches in the towns around, and a train that goes one way to to Cannes and beyond, and the other to Menton via Monaco, and onwards to Italy.
Just two of my suggestions. Less expensive areas are around Cadiz, Estepona, Tarifa, Tarragona, Valencia in Spain.
My solo trips have been to Bilbao,San Sebastian, Bayonne, Biarritz, Padova, Bologna, Salerno, Carcassonne, Narbonne, and many other places. But I am not a sun bed person, which is probably reflected in the places I go to!