No no no no...
You're all close, but not quite there. (well, yaroslav was just about right)
The very first city has number 0 (00000000 binary, with computers, counting almost always starts at 0, not 1)... From there on through the 255th city (11111110 = 254).
The "256th" city can't be built because that's what the NONE value is assigned to. That is, unit support is saved as the city number it is supported by: 0 for the 1st city etc. but 255 if the unit is unsupported.
And, of course, as yaroslav pointed out as well, while the total maximum amount of cities is 255, the per civ maximum is essentially 254 (even though you might get 255 if one of your opponents is still wandering about with a settler).