As others noted, it depends. Mostly, it depends on how large your core empire is going to be, what shape it will be, and what your strategy is.
On Regent, Standard Map, Republic, non-Commercial civ, cities connected to trade network, before constructing courthouses or the FP, your OCN is 20 (for "rank corruption", C:r) and distance corruption, C:d, rises at 1% per tile from the palace. (OCN falls to 18 in Monarchy (-10%), but I'll stick with Republic because the numbers are easier.) That means that each additional rank a city rises increases C:r by 2.5! If you space your cities at 4-5 squares distance, your first ring of six cities will have C:d of 4 or 5%, and C:r from 2.5% up to 15%, for total C (C:%) of 6.5% up to 20%. Your second ring of cities, 8 cities uniformly spaced at 8 tiles from the capital, will have C:d of 8%, and C:r of 17.5% to 35%, for total C:% of 25.5% to 43%.
As is clear, for each city C:r is much larger than C:d. So any FP effect on C:r will be far more important than the C:d effects.
So the best advice is: to minimize the effects of corruption, don't worry so much about the one city with the FP. Worry more about the other 25-40 cities you build, and make sure that you concentrate your most productive cities around your palace. City rank itself is a scarce resource - don't spend it on unproductive and unnecessary cities close to your capital.
That said, players are always worried about the FP placement, and it SEEMS like it should matter a great deal, even if it doesn't. So here's my FP-placement advice.
By now, you have 15 cities in your core, and you should consider the FP and courthouses. The FP does two things:
1. It raises your OCN, so EVERY city experiences lower C:r. Those cities that were over the OCN but are now under it experience the biggest reductions of all. Howerver, the FP does not affect ranks directly: ranks of cities close to the FP are still calculated based on distance to the PALACE.
2. It reduces C:d for those cities closer to it than the capital.
In a very large empire, placing the FP farther from your palace, gives you more benefit because it will reduce C:d for more cities. If your empire is a regular ellipse, you would get the most benefit to C:d if your FP and palace are near the foci (i.e., both on the long axis, about halfway between the center and the perimeter).
BUT! If it's too far away, the cities around the FP will get swamped by C:r - they will all be at the MaxC limit (90%, 80% w/ courthouse). The FP city itself will still enjoy MaxC of only 20% (10% w/ courthouse).
So where does it go? Well, the tricky part is that you have to decide where you are going to build (or conquer) your next 15-25 cities, because you don't want to start a new core of large, highly-improved, very productive cities to take advantage of the C:d reduction, but then end up backfilling or conquering so many small unproductive cities closer to your capital that you raise C:r in your new core to the point that the cities are net drains on your empire! (This is also why palace jumps can be ruinous if you haven't considered what C:r will do to your older core cities.)
In our hypothetical game, building courthouses in every city and the FP will raise OCN to 32.5. We've already got 15 cities, so we can build another 17 before C:r gets out of hand. You could build a second core of 15 cities, but then you'd have to make sure that you don't build too many more cities in the first core (i.e., a third ring) because each third-ring city would still be closer to the palace than the second core, crippiling your second core with high C:r. You also couldn't build many 'coastal defense' cities along your coasts that you don't intend to improve, and you'd want to raze every captured city that's closer to your palace than your second core.
The best bet is to centrally locate your palace in the area of the continent you are on, then expand to the coasts. Plan your second core to use all the remaining cities before hitting OCN for the map/level/gov't you are in (including courthouses and FP). In the example above where OCN = 32.5, if your first core gets out to a third ring (i.e., about 25 cities total), you'd only put seven in the second core, with the FP at the center. That way you avoid the conquest/backfill problem. That should ensure that your 30 cities are all in good shape.
Of course, even then, C:r is ALWAYS more important than C:d. (Std map, reg, Rep...) With courhouses, C:d drops to 50% of distance, i.e. city at 12 tiles gets 6% C. With police stations, it drops to 25% of distance, or just 3%. Peanuts. Meanwhile, if that was your 20th city, it had C:r of 47.5%, dropping to 38% with courthouse (34.5% with just FP), 29% with both FP and courthouse, and 25% after adding the police station. Thats a HUGE difference: 9% in C:d compared to 22% in C:r!
? It's probably too low to matter though.
