Granted, geography takes a rather big importance when one of the things a series focuses on is the main characters' travels. Ed & Al begin their journey by traveling around in search for the Philosopher's Stone. Their objective takes a different shape some time later, but relations between people from different cities, countries and geographical and ethnic conflicts are still a key part of the story.
The world in which Fullmetal Alchemist takes place is fictional (despite some Great Britain references), although it's undoubtedly based on ours for the most part. Our main characters (and actually most of the cast) were born in Amestris and that's where most of the story is set.
central city
Central City is Amestris' capital city. The Fuhrer, King Bradley, resides here and holds the ultimate power over the country. Once Roy and his subordinates get assigned to Central and with the arrival of the Elric brothers, the story focuses almost entirely here.
east city
After the Eastern Civil War, Roy is assigned to East City. Roy recruited Hawkeye (though he knew her from long before), Havoc, Breda, Fuery and Falman here. A safer and more peaceful place than Central, where Roy was obviously appreciated. Lieutenant General Grumman (Hawkeye's grandfather) is East's Headquarters highest authority.
resembool
Edward, Alphonse and Winry were born in this little rural town called Resembool, away from big cities and as quiet as it gets. Roy and Hawkeye found the brothers here.
rush valley
"Rush Valley, the Holy Land of Automail Technicians", as Winry would call it. This is where you can find the highest quality automail and the most experienced mechanics. Winry would lately work here.
dublith
Izumi and her husband Sigu live in a southern town called Dublith. Ed and Al had their alchemy training here when they were kids.
Even though Amestris is indeed the main set for the series, as the plot thickens more countries are brought into the picture. Surrounding this country you find Drachma, Creta and Aerugo, as well as lots of desertic area (is not especified if that ground actually belongs to someone). Crossing the desert, you get to Xing, country from where Ling, Lan Fan and Mei Chan come from.
Not much is known about the other countries, but Amestris doesn't seem to be in good relations ever since King Bradley became the Fuhrer 20 years ago. What we know about Xing is some information through people like Ling or Mei, but its actual looks are still unknown.
* Scans from Perfect Guidebook 2, edited by me.
