In Sergiev Posad tourists can dine at various spots.
The terminal offers McDonald's and a Kroshka-Kartoshka (Potatoe Baby) chain restaurant nearby with local cuisine like baked potatoe, cucumber salads and garlic bread. Cafes here are the last option due to their poor hygiene and heavy cigarette smoke around.
By the Lavra you'll find decent summer open-air cafes with beer and shashlyk (grilled meat). Premium restaurants Rusky Dvorik, Nichego Lichnogo (Nothing Personal) and Dachnaya Zhizn (Cottage Life) opposite the Lavra provide the best view and English-speaking staff.
Even inside the Lavra (at the gateway) 2 cafes serve hungry tourists. Anyway at any time you can find take-away food for spontaneous street meals like most Russians do.