Well, Bombay wouldn’t be an exonym, would it? I thought the city in India was named Bombay when it was founded.
Indiana is peppered with town names from all over the globe.
Africa, Algiers, Antioch, Big Bottom, Brazil, Cairo, Canton, Carmel, Ceylon, Chili, China, Cuba, Cuzco, Goshen, Hindustan, Honduras, Joppa, Macedonia, Manilla (2 ells,) Mecca, Medina, Modoc, Mongo, Mexico, Montezuma, Morocco, Moscow, Mt. Olive, Mt. Sinai, New Palestine, Nineveh, Peru, Poland, Pulaski, Russiaville (the first part rhymes with whoosh), Sevastapol, Shanghai, Siberia, Smyrna, Syria, (Several Turkey-based towns were probably named for the bird.) Vera Cruz, Vigo, Vilas, Volga, Warsaw, and Zulu.
Warsaw is in Kosciusko County. There’s a lot of Polish-Hoosiers.
I live in Macedonia Ohio.
Been here 25 years, no idea why we’re named for that place in Eastern Europe.
I had to destroy my Yahoo public profile because I started getting 3 or 4 Serb/Croation/Middle Eastern fellas a week chatting with me wanting to marry a girl from Macedonia (Europe).
Omaha
Mt. Pulaski, Illinois.
Zion, Illinois.
New Salem, Illinois (originally New Jerusalem).
Belgrade, Missouri.
Damn hamsters lost my last post. Small world time. I read the OP and thought" there are lots of Indian names, My home town Piscataway comes to mind." Whats the odds that my not so famous town would be mentioned in the first post? Especially weird since I am so far from home right now.
I don’t know the Bible that well, but could it be that Macedonia is mentioned, perhaps as a place where one of the Apostles went and preached? It seems anyplace mentioned in the Bible is fair game.
Speaking of which, I’m told that every state has an Antioch.
Not true. The vast majority of Indians, especially residents of the city, always have and still do refer to the city as “Bombay.” “Mumbai” has always been the Marathi version of the name. Although Bombay is located in Maharashtra, the Marathi language is not the dominant language of Bombay – Hindi, English, and Gujrati are much more prevalent. Until the official name change from Bombay to Mumbai a few years ago, the name “Mumbai” was almost always used by Marathis speaking Marathi to each other. In almost all other cases (except when trying for a particular effect), people used the term “Bombay.” (The name comes from the Portuguese “Bom Bahia.”) These days, “Mumbai” is used in official contexts, but in colloquial speech, “Bombay” is still more common.
As to the larger question, I understood the OP to include English names for non-Western-European places as well as Anglicized versions of names of such places.
To that effect, not including Native American-origin names (and classifying Greek names as western European), Ohio has places named – Alexandria, Cadiz, Cairo, Calcutta, Canton, Cuba, Damascus, Delhi, East Canton, East Palestine, Hebron, Jerusalem, Lebanon, Lima, Macedonia, Malta, Medina, Mesopotamia, Moscow, Nankin, New Lebanon, Palestine, Poland, Russia, Sardis, South Lebanon, Warsaw,
Not to mention Lebanon and Versailles (pronounced ver-SAYLES).
Oh, yeah, there are a ton of places like this in Ohio –
Lima = LIE muh
Medina = Muh DINE uh
Versailles = Ver SALES
Delhi = DELL high
It was. It was also founded by the British and given a partly translated Portuguese name. The name Mumbai probably postdates the founding of the city, since it comes from the name of a temple within the city.
Whether to call it Mumbai or Bombay has more to do with ethnic politics than anti-colonialism. Recently, I saw a good website on this topic, but I can’t find it now.
As for the general question, there were lots of ways that US placenames originated and thus a variety of names from all over the world. Or for that matter, from just about anything. Fictional characters, for example (Tarzana CA).
It should also be noted that the presence of an exotic name does not necessarily mean that someone from that location was in that town when it was named. People often took names from an atlas or one that was in the news. Or consider Madras OR. It seems that name was taken from a bolt of cloth in the general store.
Well, you were told wrong. There’s no placename found in every state. The closest is Riverside, which is found in 46 states. The four states without a Riverside are AK, HI, LA, and OK. There used to be a Riverside OK which appeared in atlases up until about the 1930 or 40s.
Speaking of Indiana, I’ll mention the best hometown in the state: Valparaiso, named, of course after the one in Chile, not the one in Florida. 
Home of Valparaiso U. I’m from CP, BTW.
How about this placename? (No, I’m not going to type it out. You’ll have to look at the link.)
Not even “Springfield”?
No. Search the boards, and you’ll find posts about that. It comes close, by the time you include all the hills, fields and drainage ditches which are called Springfield.
Well, if you’re going get that liberal, you’ll find (via GNIS) there’s some geographic thing called Washington in every state. But some states will only have Washington schools, parks, mountains, or other things that are not normally considered populated places.
Kosciusko makes a mighty fine spicy mustard.
I am currently living in Tucumcari, New Mexico. The largest community in this state is Albuquerque. Other communities include Sanostee, Toadlina, Chamizal.
In my home state of Colorado, one would find places like, Arickeree, Ouray, Teluride and Olathe (I’m not certain of the linguistic history of those last two).
TV