For paella in the city itself do consider Quique Dacosta’s Llisa Negra. We had a great rice dish there during Fallas. The rice dishes are cooked over orange wood and vine shoots in an open kitchen. Chic place.
There´s also Navarro, that Pedro recommends and Lavoe Arroz y Mar, recommended by the El País food critic.
For paella outside of the center, I’d go to Casa Carmela, from 1922.
For the best grilled meats, go to Askua, or its sibling, run by the sons, in Madrid, Askuabarra.
For Sunday night dining, we head to Ricard Cameron’s casual spot, Canalla Bistró in the Russafa district, and we too love his Central Bar in the Mercat Central.
https://m.canallabistro.com/english.
Another classic place for tapas or for find dining in Russafa, much loved by locals, is the venerable Rausell.
For us a visit to Valencia is never complete unless we go to Emiliano García’s wonderful, atmospheric Bodega Casa Montaña in the old fishing quarter of Cabañal. Just terrific in every way!