So many of these I recognise and agree with, so many many more I haven't seen and would love to. I agree (with one exception) the quieter the place the better the experience. Some of the best are those stumbled on by chance and completely unexpected.
Throwing what I hope are some different ones into the mix:
Flodden battle field - utterly deserted when we visited on rainy afternoon - the landscape that shaped the outcome of the battle was still very clear.
Eastern State Penitentiary. We learned of this place from a flyer in the hotel lobby, wandered the neighborhood, had lunch at Jack's Firehouse and then went to one the creepiest places we have ever visited. It's in a state of eerie semi-ruin and was very deserted. Horrifying and very educational.
Vasa Museum in Stockholm. The sight of the looming ship as you walk in. Wow!
Delphi in Greece. Wow again. All those famous historical figures who visited, and the epic decisions they made based on the oracle. A stunning setting too.
Not really a tourist thing but an amazing experience - the botafumeiro at the Cathedral in Santiago de Compostela. A huge censer weighing over 50 kilos, full of burning incense, swung on a thick rope by 8 men across the transepts during some pilgrim masses and other services. Since it doesn't happen every day it is really quite special to see it, we were lucky as someone had paid for it to be swung the day after we finished our camino. It gets fairly low at times and is a wee bit distracting as it whooshes over your head in the packed congregation. It's been done since the 12th century, and has only fallen off the rope a couple of times over the centuries.....
Ostia Antica near Rome. Like Pompeii, but without the tragic end and all the crowds. Has whole streets with blocks of flats still standing with corner cafes. The merchants' bourse, a theatre. Fascinating and almost empty when we went.