I second the plan of getting up early when staying in a busy tourist area. Sitting outside for breakfast or strolling the streets early is absolutely one of those peacefully surreal moments - dead quiet, the stunning surroundings all to yourself, and knowing that in an hour or two it’ll be completely packed with people.
We have some amazing photos of that giant circular staircase exiting the Vatican where we’re the only people. We had it completely to ourselves for about 10-15 mins. We were there right when the Vatican opened (and our guide somehow jumped us to the head of the line to enter) but unfortunately had to leave a little early so there wasn’t a single other person around that area yet.