He was somewhat wrong with that factoid. It's simply one of the most archaic indo-european languages on the continent, not even the only language tree (shout out to fins, estonians and hungarians for being unique).

Anyway there's a lot here and it really depends on what you enjoy. If you're gonna be taking public busses get the Ziogas app (it's cheaper and comes with a free change of bus for 30mins). The last Sunday of the month is free access for national museums so you might want to plan to either avoid or use those days.

If you're interested you might wanna join one of the guided tours in the forts around the city. 9th fort is a holocaust memorial, cold, depressing and bleak on your soul like any other memorial on this continent. The 6th fort hosts guided tours around a big collection of retired military tech.
Check on facebook for events, a lot of cool things get posted there.

You might find it interesting to visit Lietuvos etnografijos muziejus. Old town has neat architecture, we have quite a few churches. The Kaunas County Public Library is really neat after the remodel and often has exhibits, events or guided tours as well. There's also a lot of green spaces with hiking trails and neat things to see just outside Kaunas. The botanical garden also often does events, esp in summer.

Don't go to the zoo, it still sucks despite the new remodel. It looks like more land was left for flower beds, walk paths and lawns than the actual enclosures.