Dovid Katz has posted a guide for Jewish tourism in Lithuania on his website, Defending History at:
http://defendinghistory.com/litvak-tourism

The Lithuanian Institute of Tourism Development has developed a  36-page tourist guide titled “Let’s Explore Jewish History and Heritage in Lithuania.” It can be downloaded at http://www.jewisheritage.org/jh/upload/publications/Lithuania_Guide.pdf.

If you want to research your family in Lithuania, you should check out the databases located here:
http://www.jewishgen.org/databases/#Lithuania
and there is additional information about Lithuania (as well as a link to the same databases) here:
https://www.litvaksig.org/

The Jewish Community of Lithuania has a website here:
http://www.lzb.lt/
They don't really have events for tourists, but if there is an event on their calendar they are delighted to have you visit.