It took me a long time to learn to love the GP. I started liking it a lot more once I realised I didn’t need to waste gold and effort trying to maximise adjacencies. Honestly, if you just place it next to your City Centre, that’s +2 for at least one or two districts. With a mountain or some jungles etc that’s a +3 Campus, with a Wonder that’s a +4 Theatre Square. Or it’s part way to a decent IZ. That’s a good enough return for adjacencies.
Other thoughts. Three Governor Promotions is very strong. It’s really hard to go past two Magnus, one for the chop and one for settlers, and one Liang for the extra builder charge. That basically lets you grab Pyramids plus one or two other early wonders[0], and yes does let your really pump out settlers with Ancestral Hall. Indeed being able to spam settlers that all give a free builder (with extra charges via pyramid) is incredibly powerful. Really hard to pass it up.
Of course, there are lots of other ways to spend your first three promotions. Not going to debate which are stronger or weaker openings, but there are many very fun ways to go.
For the reasons above, it’s very hard to go past ancestral hall. It also the easiest building to use because it does what it says on the tin - the other two buildings are a bit more contingent when they work. AH also really helps if you want to settle mid game using eg Pac Draconis or whatever it’s called.
In terms of timing, your first government and you gov plaza are a bump in era score, so I sometimes might move things around a little to maximise that. Completing T1 buildings can also be a timing issue because I’m often in Autocracy to grab wonders and build units, but don’t want the Autocracy Legacy Card. So, I sometimes build up to one turn short, then flip to Oligarchy or Classical Republic (better), complete to get the card I want and then get AH and spam settlers.
I don’t have views about T2 or T3 Buildings. I really struggle to play past about turn 150 at the moment, just because it feels like there’s more content coming that might shakeup the mid and end game. But, yeah, hard to go past the spy building just because it’s so easy to use. The Grandmaster Chapel is probably the best because it lets you buy units, but I rarely like going that direction precisely because it is so powerful particularly if you have Medieval+ unique units. The city state one might be a bit underestimated on these forums just given Levy troops is often underrated.[1]
You also have the option of not building it at all. Not saying that’s optimal, but it is a fun variation. I do find the game can have a different dimension if you just deliberately ignore certain mechanics - eg no commercial hubs, or no campuses or theatre districts, or whatever. The game also does encourage that a little bit with governments - you pretty much have to upgrade from Chiefdom to T1 government, but some T1 and T2 governments do have a bonuses that might make you not upgrade to the next level too quickly, and then there is also the negative modifiers for T3 governments.[2]
So, yeah. Love the Gov Plaza. It’s been a slow burn, but it really has been one of the best mechanics added to the game.
[0] Side bar. It’s just crazy to me that even at Immortal I can basically grab any Wonder I want Magnus (except for the Super early ones like Great Bath, or Colosseum because of how much set off is required). Chopping is a great Mechanic, but it really doesn’t play well with Wonder mechanics or SV mechanics for that matter.
[1] Hey, has anyone else notice the GP T2 buildings are also focused on military? T1 are obviously meant to be the “wide / liberty” one, the “tall / tradition” one, and the “war / honour” one. But, yeah, I’ve only just realised all the T2 ones are about war. Does FXS want everyone to be murdering each other once we get to the Medieval and or Renaissance era? Hmm. That’s kinda cool...
[2] One reason I hope a third expansion gets into stuff like ideology etc, is that it might make moving between government tiers more of a trade off. The game should really encourage play where you sort of deliberately don’t move to more advanced technologies in some situations. Indeed, you can see that idea in Humankind where there are bonuses to staying nomadic or whatever. That sort of thing just encourages asymmetric play.