Isn't the Academy yield on Stone 1

2

8

and the yield on a quarry 3

1

?
That's what I didn't really get at I suppose in my OP. The best overall yield for an Academy/Manufactory and what tiles give the best yields?
I realise there's an opportunity cost to not building a quarry there, but surely 1

2

8

> 3

1

?
Since Stone is usually found on grasslands, its base yield is 2 food 1 hammer, and when improved by a quarry you get 2 food 2 hammers, +1 hammer at Chemistry , and +1 hammer with Order's Five year Plan Tenet. So, you lose potentially 3 hammers by planting an academy on Stone.
The idea with GP tile improvements is not to maximize the yield from one tile, but to maximize the yield from a citizen working that tile with the least amount of lost yield from the alternative tile improvements (quarry, mine, farm, etc.). That is why most players prefer to plant GP tile improvements on non-riverside farmable tiles that have a base yield of at least 2 food -- that tile only requires one citizen to work the tile and you lose only 1 food by not farming that tile prior to Fertilizer.
If you plant a GP on a tile that yields less than 2 food, you need to have a citizen working another surplus food tile in order to support the citizen working the GP tile improvement. That effectively dilutes the yield from the GP improvement tile. For example, if you plant your academy on a hill tile, that tile will yield 2 hammers and 8 beakers, but you need to work a riverside grassland farm (4 food) to support both the citizen working the grassland farm and the hilltop academy -- average yield on both tiles is 2 food, 1 hammer and 4 beakers, but only the hammer and beakers are "excess" since the food just supports the citizens (no growth). And you lose potentially another 3 hammers by not mining the hill.