A direct train from Vilnius train station which will get you to the nearby town of Trakai within 30 minutes. Trakai castle is a beautiful castle surrounded by a lake. There are water sports, boat rides, lakes to swim in, and a museum within the castle worth visiting.
The guided tour of the catacombs is super interesting - highly recommend!
This is the most popular area of Vilnius! It actually declared independence from the rest of the city at one point and has its own constitution, which is translated into 70 languages. Definitely worth checking out - it has a thriving art scene and lots of really great restaurants/coffee shops. It is also the area that Paulius grew up in and where his mum lives to this day!
If you love flowers then definitely check out the botanical gardens in Vilnius University!
The remaining part of the upper castle at the top of Gediminas Hill and has an amazing view over Vilnius.