Part of it's nostalgia, I'm sure, but the main reason is that it gives me hope for the future of our species and our planet. It's kind of hard to find that in other places nowadays.
Those are very good reasons. And I agree with the hopeful possibilities the show presents. ST:TOS showed primetime television's first interracial kiss. (A big controversy back then.) And now we have a two-term African-American president. TOS used tensions between the Federation and Klingon Empire to address the cold war (I think the episode was "A Private Little War"), which has since then ended. Star Trek presents many hopeful possibilities for humanity and often, maybe not always, presents them well. I also like Trek tech too.