The country's most famous and traditional cake is called Shakotis and its history goes back beyond the formation of present-day Lithuania to when it was still part of Poland. It's kind of layer cake, with characteristic rings that give it its name. Translated literally, it would be "tree cake" for the way it looks. One of the keys to its success is its freshness, since its spongy structure makes it slow to get hard. There are chocolate covered ones and other toppings, but the most common is the traditional one. Needless to say, it's delicious! There are a variety of sweets and biscuits (Sausainiai in Lithuanian) and the best thing to do is to go to the bakeries in the centre of Vilnius and buy them by the pound. Many are filled with a wide variety of things and they all are delicious!
In the historic center of Vilnius, despite not being one of the best restaurants, it's an ideal place to try traditional Lithuanian cuisine for reasonable prices. I suggest ordering several different plates and sharing to get a taste of everything. The most typical dish is Zeppelins, which are a kind of potato dumpling served with sour cream.
If you like Japanese and Korean cuisine and you are visiting Vilnius, then I recommend you go to LABUKI. It's located in the city center, and its décor and interior, as is typical of Asian restaurants, is very minimalist. The menu is varied and extensive, as is their wine list. Finally, the food is very good and the service is excellent. Highly recommended.
In the center of the city of Vilnius we can find this nice restaurant with mediterranian cuisine. The menu is varied and includes a zarzuela dish with the recipe from Miguel Torres' sister, the Torres wineries manager. I highly recommend dining at this restaurant, nice, quiet and good.
Post Scriptum is a good restaurant on the Gedemino, the long avenue running through the heart of Vilnius. If the weather is nice, it's a great place to go and get a drink after a walk around the city. The service is quick and friendly.