That's an easy one to answer: go to any shul (synagogue, temple) on Friday night. Lechah Dodi is sung at the end of Kabbalat Shabbat (welcoming the Sabbath), right before the start of Ma'ariv (the evening service).If you want to hear a Hasidic melody for it, though, you probably want to go to a Hasidic congregation. In fact, it would be interesting to go to several different congregations, to see how many different melodies for it you heard. You see, Lechah Dodi is a lot older than Hasidism, and people have been writing melodies for it for hundreds of years.
That said, I imagine that you would probably like to find a place where you could hear a version of the melody without sitting through a religious service. I don't know what to tell you about that. I may have a recording with a version of Lechah Dodi on it, but if I do, it would be on a small-run record that I bought years ago directly from the performer.
Of course, I'd be glad to sing you as many versions as I can remember the next I see you. Two come to mind immediately, as well as a melody for Yedid Nefesh that I think has sometimes been used for Lechah Dodi, and two non-serious melodies that use the chorus of Lechah Dodi as a lyric.
It's late Friday afternoon. What an appropriate time to be asking about Lechah Dodi!
Jacob