As it is not allowed to bring beverages to the Hermitage and to eat food in the museum halls, most likely, after the qualitative long walk around the Hermitage, you will get hungry, very hungry! There is a cafe in the Hermitage, but it does not have a big selection of savory and is quite expensive. If you want to go to the shop, there will be a small one on the right side of Millionnaya street, not very far from the Hermitage.
You can see the links of restaurant search engines below, through which you can find good cafes/restaurants with food matching your preferences.
The following website is ideal for a restaurant search on the map. It is very convenient to see the names of the places, ratings, average check.
Enjoy your meal!