Archaeological Museum 8 (11-3)
Grand Master's Chapel (22) (21 + 1)
Intelligence Agency (16)
Aside from the Archaeological Museum, I think the remaining four buildings are in fact the most important ones in these ages and my personal ranking of them probably goes Shipyard > University > Grand Master's Chapel > Intelligence Agency.
The Archaeological Museum is a bit weak imo. I think at this point, given the cost of Archaeologists and the poor timing of both the Museum and the civic unlocking Archaeologists, I prefer Art Museums. I primarily build Museums for the culture, if I've found a number of cultural cit states, and both museums provide the same culture. The Art Museum doesn't require further investment to get additional value, whereas the value added by Archaeologists is not sufficient to overcome the extra cost. But I don't think the difference between the Museums really matters. They are both largely negligible when it comes to tourism, and they both provide similar levels of culture. Here, it is just by far the weakest building left and should be the next one out.
Since I upvoted the Shipyard last time, I won't repeat the upvote and will instead prop up the Grand Master's Chapel. It is impossible to not compare this building to the Intelligence Agency, and I think the benefits it provides are at this point superior to that of the Intelligence Agency in the majority of games. In a domination game or just any game with medieval era war, faith buying supplements gold purchasing very nicely to replenish your forces on the front lines. This allows you to keep up momentum and not worry about loyalty issues at all. In more peaceful games, it allows you to play extremely greedily. I know this thread isn't supposed to take multiplayer into account, but the Grand Master's Chapel is one of the biggest reasons faith based civs are so strong in multiplayer, and a lot of these benefits translate to single player as well. I don't agree with the arguments saying you can replace the faith purchasing with gold purchasing. You can always find avenues to spend your gold, so being able to buy units with faith just means you can more quickly buy infrastructure with gold. Most of my gold is earmarked towards shipyards and universities at this time anyways.
Moreover, my biggest issue with the Intelligence Agency is that not being able to spy on allies has almost completely killed spies for me. I tend to play on small or standard sized maps only, and in peaceful games, I'm allied with half the world or more. So my spies often end up not being able to find a good source of gold to siphon, and I don't think any other mission is really worth it in peaceful play. In more aggressive play, I like the diplomatic visibility that spies provide, but the Grand Master's Chapel just provides more utility in those games anyways. I think since this update for spies, I went from building the Intelligence Agency in 60% of my games to building it in less than 20% my games.