Kamakura has a good restaurant scene for a day-trip destination — better than you might expect. The area around Komachi-dōri and the streets behind it has the highest concentration of places, ranging from tourist-facing soba and set-meal restaurants to more serious spots worth seeking out.
Shirasu — small whitebait fish caught in Sagami Bay — is the local speciality, eaten raw (nama shirasu) or cooked over rice. Most restaurants in the Hase and Yuigahama beach areas feature it prominently. It is worth having if you are on the coast for a meal.
The temple districts (Kita-Kamakura, the eastern valleys) have fewer restaurants than the main town; stock up on snacks from the Komachi-dōri stalls before heading out.