If you mean the ‘64 Fair, I’m the same age as your Dad.
http://www.nycgovparks.org/sub_your_park/vt_flushing_meadows/vt_flushing_meadows_park.html
It had fallen into disrepair for the most part to the best of my knowledge. From the site linked above, it seems like it has made a come-back. FReeper ari-freedom would prolly be better able to give you an up-to-date account.
Thank you for your reply, no I miss read your original post. My father was born in Newark in 1920 and would have attended the 1939 World’s Fair. Sorry.