I think there're clear rules on how cities are partitioned into quarters or regions. You should ask your local administration on where they draw the borders. Then you could, for example, retrieve the location data of the address (latitude and longitude might work) and simply check in which region's boundaries this address is in. There's no need for a learning algorithm for this problem.
However, if you can't acquire the boundary data for the partitions then I'd try to find the nearest known region, probably by distance. Again, I see no sense in an evolving algorithm or some sort of AI here. Either you can determine the region deterministically by known boundaries or you can try to find the nearest known region. AI is imho an overkill for such a task. You'd have to constantly recalculate initially guessed region-boundaries and evaluate them and then update existing addresses of which the region is known to be uncertain. Also, you'd have to feed the system constantly with addresses of which the region is known to verify uncertain regions.
But as regions are very unlikely to change their borders, I'd just try to obtain the boundaries, like stated above, from the local administration.