Walnut Beach
I grew up right next to Walnut Beach. It is a city-owned beach with playground equipment, picnic tables, and a concessions stand. A short boardwalk will take you most of the way across the sandy beach area to the public swimming area.
Lakeshore Park
Lake Shore Park is another option beach option in Ashtabula, but also contains much more "green" areas and pavillons. The thing I remember most about Lake Shore Park were the fierce geese that would terrorize me when I had cross-country practice there.
