I always thought that the culture level would be same for all cities of a given civ, but following screenshots seems to show that it is more city specific:
http://www.civfanatics.com/cgi-bin/a...s/1-1-2225.jpg
http://www.civfanatics.com/cgi-bin/a...16-16-2225.jpg
on the last one, look at the difference between Chartres, Marseilles and Sevastopol.
None of them are limited by neighbours, but they have cultural ranges of respectiveliy 1, 3 and 2.
So, this mean... you take an ennemy city, all buildings are new (0 cultural value), this new city of you has 0 range culture...