Legolas leaving Mirkwood/the Council of Elrond

(In the movies) Legolas says that he cannot return to Mirkwood, but other than Thranduil asking him to look for 'Strider', where does he go, or live?

And if he no longer lived in Mirkwood, why would Thranduil have sent him as representation in the Council of Elrond? Or is it because he is still his son/prince?