In Lord of the Rings why does Frodo leave?

In Lord of the Rings why does Frodo leave at the end? He goes to the Elven lands, but why? I mean he has no family there other than Bilbo, and his heart truly belongs in the Shire... the Elven lands have nothing to offer him except for long/never ending life. but his friends and family are in the Shire... and when Bilbo was writing his book, he said "There has always been a Baggins living in Bagend, and there always will be." But how could there be a Baggins living there now that Frodo left? does that mean there just wont be any Baggins living there ever anymore? It led me to believe maybe Frodo would eventually return to the Shire to have a family... I would like to hear everyones opinions on this, because Im very confused and it just seems like Frodo belongs in the shire... I alway tear up at the end because its just so heartbreaking that he leaves.. it feels like a hole has been tore in my heart, and idk why. i guess its just because i grew up loving these movies and now im old enough to fully understand them... but i just dont know why Frodo would possibly want to leave... and if he ever returns..