There is, however, plenty of evidence for a huge, huge flood at about the correct time. About 1/3 of the Black Sea was dry land until about 6000 BC [1]. The theory goes that it went from essentially dry land with forests and cities and ... to open sea in as little as 2 months, which can't have been a pleasant experience for the inhabitants.

Also note that floods don't simply go in a straight line from A->B. In practice because towns are built on the more stable land, what you'd see happen is pretty much the worst possible scenario : the water would surround cities, first making most roads unusable (non hardened ones because they become mud, hardened ones because some parts of them collapse). Then the water level would rise until nothing remains above the water level. (I've got some experience living in Northwest Europe, and every 20 years or so you get introduced to this problem firsthand)

Of course, even though the affected area was huge, it was still a local phenomenon.

[1] http://en.wikipedia.org/wiki/Black_Sea_deluge_hypothesis