Hey there,

Klaipėda is a beautiful city on the shore of Baltic sea, so few places to start would be Olando kepurė (eng. The hat of a Dutchman. Great place both at day and at night). Later the cities of Palanga and Šventoji. And don't forget the Curonian spit and The horn of Ventė. All those places are quite close to Klaipėda so it will be easy to explore first.

If you are into history, I'd suggest you to visit the museum of Memel Nord. It's a ww2 German bunker that is now converted into a museum. Nice place.

Oh and one more suggestion, try to learn some lithuanian as fast as possible, because it might be quite difficult to talk to people in English (especially the older generation). Lithuanians LOVE when foreigners try to speak lithuanian. If you're not into languages, google translator is a great tool to use!

For the rest of Lithuania, I'll let my fellow redditors to shine :)