Honestly don't think the Terrace is that amazing. In the perspective that, HC can already pop his borders even before Pottery tech if he needs to, and beyond the first border pop it's largely inconsequential. Let alone it being far from the most broken thing about HC's overall kit. That's why true CRE is so great, because it applies from the founding turn of the city, you don't have to pay the opportunity cost of building ANYTHING and can abuse your free border pops to Hell and back. But I guess it's just one more thing to throw on his pile of good stuff.
Partial to Ikhandas and Ziggurats myself as I like things that are easy enough to apply very often. Shaka's AGG combo makes it a slight economic boost for the cost of a Monument, and with AGG you might want to build early Barracks just to use the trait against barbs anyway instead of teching Archery or hoping for Horse/Copper.
The Ziggurat is the earliest courthouse as well as being cheaper and combined with Giggles' cheap Libraries you can setup a teching economy/recover from over REXing in one of the most crucial time-frames of the game, and easy city placement from CRE along with an improved Axeman if you *do* find copper...Sumeria is one of my most "chill" times playing the game. If he had been ORG instead of PRO he'd be my favorite leader hands down.
Almost all of the others are very "meh" outside of one situation where it actually does make sense to apply its unique thing...like Fippy mentioning the extra culture boost on Madrassas. Sometimes I will build a Library in a border city just to help out with border wars, and as she points out, 8 total culture per turn can be effective for that purpose if you build this early building -- early.
Sometimes will whip Ballcourts playing Pacal because +3 happy is a significant chunk and usually well-worth the hammer cost if entering whip-heavy war mode or such.
Have used Hammams in the same way in Elepult wars. They may be even better depending on how crunched for happy resources you are and how long the wars go on.
Masoleums can sometimes fill a similar role in long, drawn out wars, reducing weariness AND getting a +2 happy boost is a big shot in the arm. Considering at this tech stage they are are likely to be Cav or Artillery or Tank wars, it's not as likely as simply vassaling another target for a free +1 happy.
The Rathaus is very powerful in effect, mass whipping these can turn an entire economy around. Somewhere in one of the NC games I played in I whipped just
four in a one turn and went from like a -4gpt deficit to +16 or something. But relying on getting to CoL to fix your economy (and that you couldn't do so with Currency first) for you is ignoring some blistering issues with your play.
Dikes are giant catfishes for me

Too late to really matter, and they aren't gonna make your island cities build space parts...Sure sound good on paper though. Great in the Moai city. By the time you have steam power and cities mature enough to get Levees in them, you aren't gonna need the few extra hammers (such cities probably would want to avoid being settled with coast in the first place), and in island cities, getting them in place, likely with US though you *could* whip, proves your economy is powerful enough to not need those cities to have raw production.
Citadels are extremely specific to going siege with Izzy. They also don't hold a candle to her
other unique. But the triple upgraded trebs/cannons out the gate with Barracks+Vassalage or settled GG are good fun, and having access to both options certainly does a lot to help Spain out.
Worst UB has got to be the Stele though. Comes on a CRE leader who doesn't even want it, and would have to
tech Mysticism even if he did want it for help in border wars.