As with a lot of history, there is a considerable amount of conflicting information about where the Amazons may have lived. In fact, there have been archeological finds about Amazons from all across the world. It is probable that many Amazon cultures existed.
As with many things, history is subjective, told through the stories and observations of many differing people. Their opinions are not necessarily mine, nor do I claim to be anything more than an amateur historian trying to find where Themiscyra may have been.
My personal quest was to find Themiscyra on a map. Below are some links and information I have gathered during this quest.
I started with a map of the known world at the time of Julius Caesar. I searched archive after archive of Roman and Greek empire maps.
I finally found reference to an Amazon city in Asia Minor, what is now Turkey, near (but not on) the Halys. Set on an isthmus jutting out into the Black Sea was a city called Sinope, which sits there even today (as Sinop).
Please visit the history of SINOP page I found. While you're there, click on "more maps" to view more interesting facts about ancient Turkey. .
Basically, an Amazon Queen named Sinova (or possibly Smyrna) settled and founded what was then Sinope. But while the city was walled, and easily defended, it couldn't compete with it's sister city, Samsun, which sat at the mouth of the river and was easily accessed by ships.
But this was the history of Sinope, not the history of Themiscyra. Close, but not quite what I was hoping for.
I finally found a reference to Themiscyra at "101 Amazons", a site listing the names of famous Amazons in mythology. This site claims the Thermadon and the Themiscyran Amazons were founded originally by Lysippe. This is the legend that Celosia used when founding our tribe. (The "101 Amazons" site disappeared in 2008, sorry. You can find what they wrote about Lysippe at Themiscyra.)
To sum up, Lysippe's tribe lived north of the Black Sea on the Amazon River. Her son drowned in this river and she renamed it after him. Consulting her oracles, she was given a sign to leave and found an Amazon city somewhere else. Picking up her tribe, she moved them down and around the eastern side of the Black Sea until she came to the river Thermadon. She sent 1/3 of her tribe in one direction, another third the other way, and founded Themiscyra on the banks of the river.
And that was all I could find about the historical Themiscyra. At least online. I am always looking for more information about this area during about 45BC. (It is still the rule of Julius Caesar in our role-playing time.) If you know a good link or want more information about my research, feel free to send me an email.