Great!!! We're heading there this summer. Unfortunately, the stags have discovered it but perhpas not to the extent of some of the other cities, but it looks like it didn't spoil your time.

Any particular restaurants you recommend?

Oooh yes!
We were staying in the old town so we ate in this area.
We discovered a quaint little French restaurant called Saint Germain. It's a Bistro,not big inside and we tried to book a table,but it was fully booked on the Sunday night so we ate at one of the outside tables. They gave us blankets when it got colder! We had the most succulent roast duck and the homemade cheesecake was to die for! Reasonably priced,the address is Literatu 9.
The other place we enjoyed was called Lokys where my husband had roast badger!!!! Aaaaaaaargh!!!! I stuck to roast pork which was really good and our friends had the best cooked steaks.
The bill in this place was surprisingly cheap!
The address is Stikliu 8.Theres a picture of a polar bear that hangs over the door. Just on from here, a couple of doors away,is a terrific self service cafe selling great coffee and cakes.The waitresses are dressed in black and white polka dot dresses. They also do good salads,quiches,soups etc,but we were mad for the tempting cakes so went back 4 times!The most expensive cake costs a pound each!I'm afraid I don't have the name of this cafe but it has greeen wooden shutters painted with flowers. Sit outside!
We had a very disappointing meal at a restaurant called Narutis(part of a hotel) right on Pilies where we had fish that had been soaked in a salt brine for a while but was described as fresh. Ugh!!! We really were ripped off here paying almost £40 each for 2 courses(small portions) and wine.You don't need to spend that price in Vilnius.
We had 3 long,leisurely lunches on Pilies sitting on the terrace watching the world go by -on Saturday it was watching the wedding parties go by!Fun!
So many good places to choose from. Just keep walking so you can work up an appetite!!!
On the Sunday we hired a taxi to take us to Trakai to see the fairytale castle and little Karaim houses.This was far more touristy. We would've been better to go there on a weekday.
I would go back to Vilnius this weekend if it were possible!Hope you enjoy it as much!