Morning stroll in the old town for about 2 hours, seeing the most beautiful buildings on Pilies, Didzioji, Ausros vartu, Dominikonu, Universiteto and other streets. During the walk visiting the Cathedral church with the chapel of St. Casimir, the patron saint of Lithuania. Also visiting the University complex (located in the very heart of the old town, with beautiful facades and many cozy courtyards (entrance to the complex costs 1.5 EUR per person), during warm season it's worth to climb the bell tower of the University church for stunning views of the old town, entrance to the tower costs 2.5 EUR per person).
Enjoy stunning views and picturesque panoramas of Vilnius. Visiting the Gediminas tower with little historical exhibition (entrance to the tower is 5 EUR per person.)
Take a walk along the Gediminas avenue which is the main street of the New city of Vilnius (actually it is not that new, about 100 years old). Here you can enjoy beautiful facades of the buildings, you will see some important structures like the Government building, the Parliament, the National drama theatre. There are several department and fashion stores located here so you could do some shopping or "window shopping" too.
Visit in the "KGB Museum" (The Museum of Genocide victims, located on Gediminas avenue, entrance fee 4 EUR, guided tour costs 20 EUR). In this impressive museum you will learn about the times of different occupations of Lithuania in the 20th century, about the activities of Gestapo and KGB in the country, genocide, repressions and deportation of local people to Siberia. You will see here in the basement of the building original cells of the former KGB prison. Visit here lasts about 1 hour.
Afternoon at your pleasure: shopping, resting, partying, visiting other museums like the Palace of the Grand dukes of Lithuania, the Vilnius Jewish museum or the Vilnius Paintings Gallery. Or rent an orange bicycle to explore the city using the marked bicycle routes. Suggestion for dinner: surely you would like to experience traditional Lithuanian cuisine and local brews. Right places for doing that are atmospheric traditional food restaurants like Forto Dvaras or Leiciai, located in the old town.
40 minutes ride by bus to Trakai town from Vilnius main bus station (ticket costs about 2 EUR one way) and then about 30 minutes walk along a beautiful lake to the castle of Trakai, located on one of the islands of lake Galve.
This impressive castle is the highlight of Trakai and one of the most important sites for the history of Lithuania. Reach the castle by bridge and explore the museum of history inside (entrance fee 6 EUR). It will take you about 40 minutes to see the museum. After this, if the weather is nice, you might like to go on a yacht ride (about 30 EUR for 30 minutes) on the picturesque lake Galve or to rent a paddle boat and explore the lake on your own.
Another interesting place to see in Trakai town is the Karaimu street with traditional Karai houses (Karai people are local national minority that came from Crimea and live in Lithuania for 600 years, maintaining their traditions, religion, language and cuisine).
When in Trakai you could have lunch in Karai restaurant and taste their traditional dishes like kybyn, ajaklyk or dolma and their traditional bitter liqueur.
Then you could continue your walk through the town and see the ruins of the peninsular castle of Trakai and after that head back to the local bus station (30 minutes walk) and take a bus to Vilnius.
Time for some more stunning panoramic views of Vilnius old town: you can climb up the Hill of Three Crosses and the Hill of Gediminas Grave for different and beautiful views of the city. The hills are grown with trees so you would feel like being on a hike in a lush forest and the same time you wouldn't leave central Vilnius.