Not a convention, but it is a 3-day event:
Visit Star Trek studio created by fans in Kingsland, GA. October 19-21, 2018. It is FREE and the sets are incredible! Check it out at stage 9 studios, and click on "visit", for more information. Last time fans came from around the world to visit these sets and they had added more. I visited a few years ago and was absolutely in tears at how wonderfully the full sized sets have been re-created and lovingly shown by fans, for fans. I got to stand on the transporter, visit Kirk's quarters, sit on the bed in sick bay, stand on the bridge... and so much more. If you are a trek fan anywhere in the area, and do not go and see this, all I have to say is-- "Oh my!". Costumes are encouraged. This visit will change your view of TOS forever....in a good way.