Best plan to discover Lithuania in a week

Hi Lithuanians!

I'm a Ukrainian living abroad, and I want to pay a visit to your supportive country this year, it's the only Baltic state that I haven't visited properly. I've got some week or so to spend here.

My plan is to see Vilnius and Trakai, and then I have Kaunas, Klaipeda and the Hill of Crosses saved as other destinations.

I want to ask you for some local suggestions — what would you recommend to see? Where to eat genuine local food? Is there a preferred way to travel around?

And, maybe the most interesting question — any sources which would help me grasp some basics of Lithuanian?

Sorry if redundant, feel free to send me to fo if yes.

See you soon!