My question is how much it actually matters. If you can get a 'better' city spot that isn't beside a river what are you giving up? Along a similar vein, how important is it to build the national wonder with the same bonus? How important is it to stack other buildings in the city with that wonder? Heck, how important is it to build an early wonder with great person generation built in?
I built an early pyramids wonder in my quick asynch game and 67 turns later I got a great engineer out of it. That let me rush buy another wonder (Angkor Wat) that I had no hope of building otherwise. It also came with a great engineer point, so after 67 more turns I could have had another great engineer! With no other source of great people I could have turned an early pyramids wonder into 2 more wonders for free!
Or is it actually for free? It turns out great people are generated in a bit of a weird way such that there is a cost to getting a great engineer. There's a system in place such that each subsequent great person of a given type costs more points to generate. The first great artist costs 100, the second costs 200, the third costs 300, and so on. The twist is the scientists, merchants, and engineers all share the same cost pool. So if you get a great engineer for 100 it bumps up the cost of your first great merchant to 200. Get one of those and now the cost of a great scientist is 300. If you hadn't picked up that engineer or that merchant then those 300 great scientist points would have gotten you 2 scientists, not 1.
This is a big deal because great merchants are garbage. Money is really good, don't get me wrong, but the sheer amount of stuff given by an engineer or a scientist is a lot larger than the amount given by a merchant. I guess if you have a game plan around a lot of money (diplomatic victory) then getting great merchants can be a good way to get some cash along with some city state influence. I guess the big thing is just to recognize what you're going to want and then try to avoid getting the stuff you don't want.
The other weird aspect of the whole thing is each city generates great person points for each type of great person for themselves alone. The points don't get pooled together between cities. So you can get yourself into a situation like I'm in where I have 4 cities generating 3 great engineer points and another generating 2. So I am making 14 great engineer points and if they were all consolidated I'd get a great engineer in 14 turns. Instead I'll get one in 67 turns. I will get one 67 turns after that, and then 67 turns after that. Consolidated I'd have to wait 28 turns, and then 42 turns. One of those things is _way_ better than the other.
Of course the tricky part is you can't just go and consolidate it all in one place. You can get a few great person points out of wonders but for the most part you get them out of specialists. I have so many cities making small amounts of engineer points because all of those cities and manning workshops in order to throttle my population growth while I deal with happiness issues. So I'm not really trying to get great engineers. I'm trying to get 0 food and 2 hammers! It is conceivable to imagine stacking wonders all of the same type in a city though, and then making sure that city ran the right specialists too.
But what about gardens? Considering how the costs of the great people escalates, do they even help much? How should I work such a thing out? The easiest is probably to look at the non-pooled ones first. Great artists, musicians, and writers can only have points generated from one national wonder so they're restricted to one city each. Let's compare the number of great writers generated from a city with different amounts of bonuses... Assuming you fill up the specialist slots you'll be making a base of 7 GPPpt. Here's the turn number after building the writer's guild where you'll get the Xth great writer.
Going from base to +25% means you'll sometimes be even on number of great writers and sometimes be up a great writer. You're never going to get up a writer, at least not in the first 300 turns. And for the most part you're going to spend more time even than you are up a writer. On the other hand, if you get both a garden and a national epic and compare that to a city with neither and you'll get up a full great writer after 143 turns. What about if you do have a garden in both cities... How important is it to build the writer's guild in the city with the national epic? It's pretty similar to the first case. You'll never get up a full writer. You'll sometimes be ahead 1, and you'll sometimes be even.
Now, you are still getting something. Assuming you make a great work out of each writer you'll be up 168 tourism and culture over the first 200 turns when you compare base against garden. It's a 16% boost in culture and tourism.
But is that worth worrying about getting a garden? Well, you'll be getting the 168 tourism from the great writers but then you'll be getting a similar boost for great musicians. And for great artists. And you might get the boost for the pooled great leaders too, assuming you have a garden in a city with lots of specialists and/or wonders. Is your capital really going to have room for all those specialists? It needs 6 just for the artists/writers/musicians. Then to get even more specialists for all that other stuff too? Feels a little restricted.
You can definitely do it. A full tradition policy tree, a lot of food, maybe some internal trade routes... And if you're going to do it, you want it to be your capital, because of the monarchy policy which halves the unhappiness for people in your capital. And all those people will do good things for your science production too, so it feels really strong. It's not the only way to go, but it is a good way to go. If you do go that way you're going to want a garden. So I think if I'm going to be trying for a big capital I'm going to want to be on a river. Or I'm going to need to rush hanging gardens. The 6 food from the hanging gardens will help with getting a big enough city to run all the specialists, too!
My gut feeling is a 25% boost is nice, but it's not critical. But there are a bunch of them, and if you can stack up quite a few of them you do get a pretty significant bonus. I'd need to be getting a lot out of it to want to settle someplace that isn't a river with my great person city.
I can see building a city just for great people that isn't the capital. If I can't get my capital on a river and if I can't get the hanging gardens then founding a city somewhere else, on a river, and giving that city the national epic and all three guilds is pretty reasonable. You might even be able to stack an extra 25% boost in there by rushing a wonder with a great engineer or something?
But if I get a chance I will definitely keep trying to found my capital on a river. And I'm going to keep an eye on what cities have specialists in a market or a bank to try to cut down on my great merchants. I'd really rather get extra great scientists or engineers!