Ashtabula has a bunch of beaches, but most of them are private. Watch this video of Ben Gravy attempting to surf somewhere in the vicinity. Yet, there are at least 3 known surf spots accessible to public:

Walnut Beach Park - sandy beach, may get waves on W, SW and strong NE winds. Watch video for sample conditions in April. Established kiting and windsurfing spot.

Geneva State Park - nice sandy beach.

There is only chance for surfing on W, SW, strong NE winds.