Novgorod Restaurants and Cafes.

Eating out is quite cheap in Novgorod. Even in the most expensive places you can dine for $5 US. The most known restaurant is "Detinets", located inside the Kremlin, you can also find restaurants around Kremlin in the garden, and at the hotels (for example, "Volkhov" or "Intourist"). If you're looking for something cheaper, you can try cafes and bistros, where you can dine for $2 US.
Most restaurants and cafes stop working at 22.30 - 23.00.

Finally, if you're hungry and everything is closed, you can try a 24-hour food shop "Adept" on Karla Marksa (Карла Маркса) street, #12.

If you want to try the berries from the region, walk down Karla Marksa street from the railway station, and there'll be babushkas (old women) selling many kinds of berries really cheap.

Detinets Restaurant.
Located inside the Kremlin, in Pokrovskaya tower, this restaurant serves the best Russian food I've ever tasted. The restaurant is named after the Novgorod Kremlin - Detinets. You can sit inside the tower, or just outside, under the elm trees, eat delicious Russian food, and enjoy the view.
The dinner (a soup, a meal, dessert and a drink) will cost around 150 roubles ($5 US). Try fish soups (for $1.5 US), fish in the old Russian style ("Ryba po-starorusski" - "Рыба по-старорусски") - sudak filet and potatoes cooked in a boullion - $2 US, Russian pancakes with honey ("Blyny s medom" - "Блины с мёдом") $1 US.
A must-try is a traditional Russian drink - Medovukha ("Медовуха") - a honey alcoholic drink that's brewed in the restaurant. In Novgorod they prepare it the best way.
They start cooking after you order, so it'll take around 40 minutes for the food to be ready (you can walk around the Kremlin, while waiting, or just go for a swim on the beach 5 minutes away).
Address: Kremlin (Detinets - Детинец), Pokrovskaya tower.
Directions: when you walk inside the Kremlin from the side of the city, turn right and walk around 200 meters, the restaurant is in the second white tower on your way. Phone: (81622) 7-4624, (81622) 7-3015. Open hours: 11.00 - 23.00. The bar works until 23.45.

Baskin Robbins Ice Cream Cafe.
An ice-cream chain, lots of different kinds of ice-cream for about $1 a cone.
Address: #5/2, Gazon (Ãàçîíà) Ul.
Directions: when you walk out of the Kremlin to the city, walk through the square and turn right. Walk 50 meters and on your left there'll be the cafe. Phone: (81622) 7-7521. Open hours: 10.00 - 23.00.

Ilmen Cafe, Bistro, Restaurant.
The cafe is a great place to have a midday snack. Russian cakes ("pirozhok" - "ïèðîæîê") just for 5 roubles ($0.15) - try apple and lemon cakes, various salads starters for 8 roubles ($0.25) for 100 grams - try a tomatoe stuffed with cheese and salad, fish and meat are for 16 roubles ($0.6).
Just next to the cafe, there's a bistro, something like a cantine. Really cheap: for example, you can eat a meal like potatoes, salad and meat / fish for only $2.
Just next to the cafe and bistro there's a game place: air-hockey.
Upstairs there's a restaurant, and a complete meal there will cost around $5.
Address: #2, Gazon Ul.
Directions: as you walk out of the Kremlin to the direction of the city, walk through the Sofiiskaya square to the big building and turn right. Walk along this street (Gazon), until the end and on your right you'll see a 2-storey building, this is "Ilmen". Open hours: 11.00-21.00 (cafe), 11.00-23.00 (bistro), 14.00-2.00 (restaurant).