All the maps on the internet show the Medes south west of the Caspian sea.
http://courses.wcupa.edu/jones/his101/web/pix/persia-s.jpg
http://www.historywiz.com/images/neareast/neareastmap.png
(sorry about the horrible english)
The region and its history is very complex, I am not a Historian, but I noticed nobody has replied, so here comes my quickly typed response. I hope it helps a bit:
The map doesn't show where the Medes came from, but where they ruled. The placement of the word "Medes" on a map isn't indication or proof of anything, it's just placed there out of convenience. And even then, it corresponds to where Kurds lived/still live.
The Kurds are an hetereogeneous nation. This means they are not descendants of a single ancient tribe or nation, but of multiple ancient Iranian tribes (of which the Medes are one, perhaps the largest).
The Kurds claim to be descendants of the Medes is based on the following facts:
Area Medes originated from corresponds to where Kurds still live, thousands of years later.
Modern Southern-Kurdish is directly related to the language the Medes spoke.
Until the 10th century, some foreign sources kept referring to some Kurds as "Medes". These references declined over time, until "Medes" vanished from the relatively modern records.
Most of the Medes' important cities and burial grounds are located in modern-day Kurdistan.
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The third point is the most convincing to me. It shows that the only thing that has changed is how Kurds (some previously known as Medes) call themselves (or are referred to by others).
The Sassanians are also believed to have had Kurdish origins. The first Sassanian Shah is even called a Kurd by the last Parthian ruler in an ancient text, and most of the Sassanian era structures are located in Kurdish areas (in Kermanshah alone there are hundreds of Sassanid-era archaeological sites).
In short; the Kurds are not a homogeneous nation e.g. like the Japanese.
Kurdistan is a very mountainous area, this has allowed different Kurdish cultures and other nations to survive while other ancient nations have perished.
A good example is how the Aramaic language, the language of Jesus Christ, managed to survive in Kurdistan until this very day, while it went "extinct" everywhere else in the world.
