Europos Parkas- An open-air contemporary art museum with thought-provoking sculptures from artists around the world. I highly recommend you make the trek, and spend some time in this art-filled natural area.
Lithuanian Theater, Music & Film Museum- A great collection of musical instruments, theater sets, vintage cameras and more! A bonus is that the woman working there is so thoughtful and excited about the exhibits. She spent some time in Chicago, and she can give you extra information in English.
Rasos Cemetery- The oldest cemetery in Vilnius. It's really extraordinary with many unique tombstones set amongst rolling green hills.
Gediminas' Tower of the Upper Castle- An amazing view of the entire city of Vilnius can be seen from up here. It's not a bad climb to get to the top, but they also have a funicular that will take you. I especially enjoyed the remains of the castle; It's simple and majestic at the same time.
Vilnia River- One of my favorite things in Vilnius was going down to this river and dipping my feet in it. It is ice cold, which is perfect on a hot summers day, and the current is just strong enough to feel like it's massaging your feet. The location by the Bridge of Uzupis also had many rock sculptures protruding from the river.
Forto Dvaras- I was told by locals that this is where I should go for traditional Lithuanian food. It is a chain restaurant, but I found the food to seem authentic and good. I had pig ears and cepelinai (zeppelin), which is a large dumpling filled with your choice of meat, cheese, or mushrooms and usually topped with sour cream and bacon.
Keule Ruke- A BBQ place in Lithuania? I know, I thought the same thing, but considering they are very far away from the south of the US, it was surprisingly tasty. It's a small group of young people running the place that are professional, nice and educated about the food they are making.The decor looks like a cute juke joint (I know, in Lithuania?), but it works. Besides, you can't eat zeppelins every day!
La Boheme- A French inspired restaurant in a beautiful setting. A great place for a romantic evening, and it's right next to KinoPasaka movie theater.
Uzupio Sardinija- A charming café/bar where you can have a drink there or buy a bottle of wine to-go. The man that runs the place is incredibly welcoming. It was the best place I went to for wine in Vilnius. It has a local clientele.
Zalia Zasis- A fantastic place to have a glass of wine by the river.
I stayed at an apartment in Užupis. The area has an artsy vibe and is convenient to many of the museums and interesting sights in the city.