The first time we went to Rome, in 2006, our apartment was on Borgo Vittorio, which is close to St. Peter’s. It runs parallel to the Borgo Pio, which is a relatively famous street.  (A good history of the Borgo area). Michael got up early every morning to go to Mass at St. Peter’s – I never did because a) I really didn’t want to get up early and b) “me” getting up early involves not only “me” but others who needed their sleep. He always spoke about what an interesting experience it was.
And it is!
This time, I found myself rising early most mornings, completely without prompting. Amazing. I went down to St. Peter’s early twice, once on Wednesday and then on Friday.  I left the apartment about 6:30, hopped on the 870 and walked the two or three blocks over to St. Peter’s.
Because St. Peter’s is so huge, I don’t think the crowds in the Basilica itself ever get terribly oppressive (as opposed to the Museum), but it’s still a very worthwhile experience to go early, when the place is practically empty. First, the security line is nonexistent. Secondly, it’s a marvelous thing to be able to watch priests from around the world come in from the sacristy with their servers, sometimes accompanied by a small band of family, sometimes met at the altar by a small group, often nuns, to the side altars to celebrate Mass.
With my little camera, I took a couple of videos. They’re not great. In fact, they’re not very good at all, but perhaps you can get a sense of it. The first two are just shots of the various altars with priests celebrating Mass, and the last one is a 360 shot of St. Peter’s at about 8am, to show you how empty it is, and why that’s a good time to go for a more peaceful experience:

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And yes, the Masses are all celebrated ad orientem, and everyone seems to survive and they even seem to, you know, “participate.”
The disadvantage of going during this period, when the priests are celebrating at the side altars, is that you can’t get close to the side altars to really get a good look at the art. But I think that those Masses only go on for so long – perhaps not even longer that 8:30 (again, a more knowledgeable person can fill us in), giving time to take a look before the crowds really begin.

One more thing: Michael had mentioned at the time that the Masses at the tomb of Blessed John XXIII always had the greatest in attendance. I found that to be true as well: