What to do:

Visit the old town. Walk the touristy streets, since they are really beautiful.

The cat cafés are nice.

There are locals selling home-grown food in front of most super markets, it's fresh, healthy, delicious and cheap.

Kalvariju turgus (a market) is a cool thing to see, especially if you are up early. Check when it's open, though. I think on Tuesdays...?

Concerning safety: It's like visiting Berlin. We don't have no-go areas or anything, but you should, like, pay attention to the world around you and if something feels off, get out. It's very unlikely that you will get stabbed, but there is a real risk of returning without your wallet.

What not to do:

Praise the UdSSR, that's like praising the Third Reich in Germany. Also, you can buy UdSSR memorabilia, but it's forbidden to wear them.

Praise Russia.

Praise the Polish-Lithuanian commonwealth or equate Lithuanians to Polish, especially if talking to older people.

Try to bribe anyone- will result in significant legal trouble.

Annehmen, dass die Litauer kein deutsch können, das können nämlich erstaunlich viele!

Some finer tips:

When in traffic (even as pedestrian or sitting in a bus), you have to indicate with your energy and body language what you intend to do. Like crossing the street, even on a zebra strip, if you stand there relaxed, nobody is going to stop for you, but look as if you wanted to cross and you wil be able to. Hard to explain through text, but if you look out for it, you will notice it quickly.

If you drink Schnaps with the locals, never pour your own drink. You pour for them, they pour for you.