I have a 9:30 Scavi tour on a Tuesday and Audience tickets the next day on Wednesday. Inside the Basilica and up the dome is a must. Which day is best for adding a museum visit? I am concerned about being exhausted, but wanting lots of time in the museum.
Congrats on your upcoming visit to Vatican City, teachn6! And two thumbs up in booking the Scavi pilgrimage. It's a moving experience, and I highly recommend it to anyone I talk to about my Rome trips.
Based on what you have planned, it sounds like Tuesday would be your best option to visit the Vatican Museums. The Scavi pilgrimage lasts 1 hour which would give you all afternoon to enjoy the museums. Attending the papal audience on Wednesday will be a time-consuming experience since you will want to arrive early for seats, etc. Thus, Tuesday makes more sense.
A clarifying note... The Scavi pilgrimage ends in the grottoes underneath St Peter's (actually the layer of the church that is the original medieval St Peter's Basilica - pretty cool!). When you exit the grottoes, you'll run into the folks who are exiting the Sistine Chapel. It's simply how they direct the flow of traffic within the area. To get to the Vatican Museums after the Scavi pilgrimage, you'll need to walk around to the opposite (west) side of Vatican City, about a 30min walk. This would be a great opportunity to stop for a snack or even walk around the Prati neighborhood. After exploring the neighborhood, find a spot for an early lunch, then enjoy all afternoon at the Vatican Museums. Well worth it, and you'll love it! Hard-pressed to pick a favorite, but the Gallery of Maps is so cool.
Happy planning!