For amenity wonders, you need a fairly large empire for them to be worthwhile, 10+ cities.
Personally I think Petra is garbage without lots of desert hills. A 21
2
tile isn't very impressive. If you could farm desert tiles, that would be another story, but you can't improve it all unless it's a hill, in which case it's a pretty sweet tile. Not worth it imo. Built it in my Rome game, was so excited, then found out I can't farm all that flat desert I had.
I think all of the unique improvements can be built on desert and tundra, so if you have a civ like that or the city state ally that lets you build colossal heads it might be worth it. Still very situational.
I put it under a general tier because appeal also helps cities overall (housing, etc.).Eiffel Tower should definitely be mentioned for cultural victory. Appeal translates directly to tourism for national parks and and seaside resorts.
For amenity wonders, you need a fairly large empire for them to be worthwhile, 10+ cities.
Personally I think Petra is garbage without lots of desert hills. A 21
2
tile isn't very impressive. If you could farm desert tiles, that would be another story, but you can't improve it all unless it's a hill, in which case it's a pretty sweet tile. Not worth it imo. Built it in my Rome game, was so excited, then found out I can't farm all that flat desert I had.
I think Broadway, Hermitage, and Sydney Opera House are extremely weak, especially considering that they're absurdly expensive. The Great Library is near-useless, boosting all ancient and classical techs is pathetic. If it granted a % science boost instead, like Oxford, that would be good.
Big Ben and Forbidden City are way better than Potala Palace and Alhambra, I think. Once you get past the classical era or so, economic slots are much more helpful than diplomatic or military policies. When I build Potala Palace I usually find myself with nothing good to put in the slot.
Great Library is just such a strange spot, you've already researched everything by the time you get close it it. It needs to be much much earlier in the tree, and much cheaper to build.
I also agree that the cultural building you mention are poor. This is mostly because the culture game at the moment is all about national parks, seaside resorts, and archeologists. Perhaps when the inevitable great artist/musician buffs come through they will be more worthwhile.