A good time to visit St Peters is as soon as it opens up in the morning. This is around 7 am I think. This is before the tourist hordes descend on the Vatican since they are all still waking up or having breakfast. YYou have to get up early to do so but it is quite a different place to view almost empty. When I visited there were a few small masses taking place in corners of St. Peters but that was it. Also seeing the rays of the sun enter the basilica through the windows of the front entry is another highlight.
-----thread brings back so many memorable moments-----
Thanks for the tip, my son will be there this summer and I sent your comment to him....he will have nearly 5 weeks in Rome, do you have any more suggestions?