In Vilnius for vacations.

Hello, I'm Igor from Italy.
'll be in Vilnius from 21 to 25 june, and I would like to know more
about this wonderful city. If someone can help me, or give some advice, how I can arrive from airport to center city. And should be wonderful to meet up with local's people to hang out for a drink and to visit some places together, like the trakai castle, the old city, and having an aperitive together. Who would like to make the company?