Having just completed the camino Portuguese, on the day that I got there I just wanted to sit and cry in the cathedral and have a quiet time to reflect on my journey. Instead I was surrounded by crowds of tourists talking and taking photos and a security man trying to keep them quiet by talking into a microphone.
I wondered if it would be an idea to reserve an hour a day just for pilgrims to be in the cathedral. Even if it was at 7 am i think it would be worth it as pilgrims arrive in santiago in such a different space from tourists and we have spent weeks walking to that one place. Wouldn't it be good to honour that and give us some time to ourselves in the cathedral?
Setting aside the Cathedral for only pilgrims is never going to happen...period. So, I have two constructive suggestions:
1. As others suggest, try a side chapel in the Cathedral. Most are open most of the day. the Chapel of the Communion (Capilla de la Comunión) last one on the left, before the main altar, is open all day for Eucharistic Adoration.
Just as a BTW and FYI, for non-Catholics, Eucharistic Adoration is among the most solemn practices in the Faith. Catholics believe that the consecrated host IS the Body and Blood of Jesus Christ. So, clearly, the large host exposed in the monstrance atop the altar is deserving of the highest manner of respect and decorum.
So, this is IMHO the quietest chapel, all day. It has glass doors, and the security guys do not permit talking and gawking. Observant folks, or people seeking a quiet place for mediation, will come to this chapel, knowing that the security folks enforce solitude.
2. Failing that, go to the Pilgrim Office. Just off the entry vestibule off Rua da Carretas, the chapel is to the left. The Camino Companions program holds a few mediation sessions there during the day. These are scheduled and posted. However, when not in use, this chapel is an outstanding and quite place to just have a cry or spend some private time "with the Boss."
While I volunteer at the Pilgrim Office, I usually take overwrought pilgrims, and pilgrims in physical pain there. Most folks, even non-Christians find it very comforting. I even supply a packet of tissues...
You can close the hallway doors if the crowds coming to get their Compostelas annoy you. Only pilgrims with credentials are allowed past the security guards into the building. The sole exception to this has been allowing tourists to see the chapel. but, there are VERY few tourists.
I hope this helps.