Moyes first day on July 1st. I'd expect a press conference that week by then hopefully the transfer that everyone is talking about non-stop gets done and as said above, for some positive stories be in place for his conference with the media.
Rooney was scheduled to have talks with Moyes this week so again, Moyes' press conference will probably be overshadowed by transfers, squad make up than his actual appointment.
I'm intrigued by Moyes as his approach to the media as boss. At Everton, he was fairly personable whilst maintaining a distance but SAF was very strict with the one news conference with the TV/Radio/Newspapers (think he did do a Sunday briefing for some) rather than seperate briefings but I hope Moyes does things differently whilst responding to unfair criticism sternly.