I used the ProQuest historical database of NewYork Times issue to find the first mention of some phrases as follows:
1."ARPAnet"
NewYork Times; Jan 19, 1933 (Display Ad 34-No Title).
2."NSFnet"
NewYork Times; Jun 18, 1983 (Stock Quote 1-No Title).
3."Internet"
NewYork Times; Sep 20, 1851 (Classified Ad -No Title).
4."Cyberspace"
NewYork Times; Nov 29, 1985 (Science Fiction by Gerald Jonas)
5."National Information Infrastrure"
NewYork Times;Jan 3, 1952 (Rearming Forges Ahead as European Countries raies Defense Budget)
6.World Wide Web"
NewYork Times; Dec 22, 1882 (Article 8-No Title)