I made my good Christian Pilgrimage to see the bones of St Peter recently. Alright, maybe it wasn't as a Christian, but it's something very sought after by some Christians and Catholics. In my case, I was travelling to Italy, including Rome, seeing the Vatican anyways, and my wife ran across the tour. Normally it's way too busy to get in and you have to make reservations months in advance. Since we were travelling in November, we got in with like six weeks notice. I was excited. I love history, and I have to say that the tour did not disappoint.
It's called the Scavi Tour. About 12 people can take this tour that goes two stories below the floor of St. Peter's Basillica at a time. Only 12 because the rooms and hallways are small. It's also kept humid to keep the bricks intact because it's an ancient Necropli or Crypt so you wouldn't want anymore people down there to add to the heat. Again, this was a November tour. As a side note about the conditions there, you really do need decent shoes there. The old floors are terribly uneven and not always visible. But on the link that I provided you can also see pictures and take a partial virtual tour.
The history is fascinating and my experience was with a great guide. The story of the necropoli takes some twists and turns. The short is that Christianity not being legal in the days of Peter's Crucifixion, the early Christians had to "hide" his body. So they chose a necropolis that held many families. There were 10 or so rooms in the Necropolis and one held 120 sets of human remains. The difference at the time was the Peter was intact as cremation would be a denial of the faith that Jesus would return to raise the dead. So Peter was buried in the wall of the necropolis and his grave was not marked with anything that indicated who he was or what his religion was. If his body was found he would have been tossed into the sea as that had some sort of after-life effect in the pagan religions. The barely decipherable markings that were placed on the wall were known as Graffiti and so the wall became known as the Graffiti wall. (some more details are found on the link) This along with the obvious pagan religions represented in the necropoli threw those looking for Peter off the trail. For example, Horus is on one of the walls in the Vatican Necropolis if you can believe that.
Without babbling on forever, the second Basilica was built in the 17th century over the necropolis. The top of the dome at it's center is directly over that Graffiti Wall location where Peter was buried until modern times. So think about that. The base of the Vatican is built on Paganism. Not only is it mythically an assumed fact among us that the savior god Jesus is based on other pagan gods, it's architecturally a fact as well. Modern Christianity's holiest place and holiest bones physically share space with pagans and the image of a pagan god, Horus.
The "goal" of the pilgrimage is to view the bones of Peter and pay respect. While my wife and I didn't pretend to pray, it was clear that people were taking it seriously. You don't see much of Peter. You can just barely see the end of what I assume is one of his tibia's since he was cut down from his upside down cross. He didn't feel worthy to die in the same manner as Jesus so he requested to be upside down. The overall story is fascinating. Seeing the tombs and getting the tour is well worth it. I think that it was even free. I would suggest visiting the Vatican. Ignore what it means and what it "cost" to build it. Take in the history and marvel at the art and/or architecture. At the top of the dome you get to see great views of Rome. In the Sistine Chapel you get to see Michelangelo's work that is still fantastic even if the subject matter doesn't speak to us. You'll know more for simply having gone. In my experience with my two guides (we also did a Vatican tour with a Vatican employed guide), they were both honest about the history. One of them even noted the sordid past of many Popes. It halfway stopped my mind in it's tracks. "Did I just hear that?" Plan ahead if you make the trip. You may need to make the reservation months in advance.