What do you plan to do there?
For me, a great time to visit St. Peter's in early morning, before there are lines for the security check, before there are lots of people in the church. Then climb up to the dome. There's limited capacity, so if you don't go up soon after they open, you can get stuck in a long line. I went in February, about 1/2 hour after they opened - no line and I climbed at my own speed (much of the ascent is narrow and you can only go as fast - or as slow - as the people ahead of you, no passing possible). An hour later or so later when I came down, there must have been a hundred people in line to go up.
From St. Peter's, it's a 10-15 minute walk to the Museums. There's a one-way route to walk through the museums (which are huge). Do you want to spend a lot of time looking at the incredibly extensive and varied collections? Or do you want to see a few highlights and the Sistine Chapel? The Sistine Chapel is almost always really crowded, but you're looking up, so it doesn't really make a lot of difference. So if you don't take a tour and just want to see a few "bits" it doesn't matter so much when you go, as long as you have a reservation so you don't spend a long time in the security line. If you want to spend a lot of time seeing the museums, Thursday and Friday are usually less crowded. If there's a papal audience on Wednesday morning, the museums may not be so busy, but when it ends, a lot of the crowd will head for them. My first visit was on a Monday in February - I knew Monday wasn't a good day, but it was the only day I could do it. Some of the galleries were so crowded, it was difficult to walk through them. BTW there's a one-way route through the museums, more or less ending at the Sistine Chapel. You can backtrack (before the chapel), but if it's crowded, you'll be like a spawning salmon - upstream against the current.