City names. Pronounced a distinctive way by residents, but a different way by everyone else.
Examples:
Baltimore
Locals: Bawl-mer (Merlin. Hon. ;))
Everyone else: Ball-ti-more
Louisville
Locals: Loo-ah-vull (kinda all muddled together)
Everyone else: Loo-ee-ville
Others?
In Australia: Melbourne is Mell-bun
Elsewhere, it’s Mell-born.
Presumably, we needn’t mention Cholmondeley Castle in England.
Lancaster, PA.
Locals: Lank-aster
Others: Lan-Cast-er
In Spain, Oviedo is ov-ee-ay-do. In Florida, it’s Oh-veedo (or ahveehda if you’re a bit of a redneck.) I expect there are other Oviedos in the Spanish-speaking world and probably elsewhere in the US, but I don’t know how they are pronounced.
Glasgow rhymes with cow in the US, because… well, because we don’t know any better.
Newark, OH.
Locals: Nurk
Others: New-werk.
Worcester, MA
Locals: Wuhster
Others: War-chester
Most in the UK would say it the local way.
Maybe in the US, but pretty much everyone in the UK pronounces it really close to the local way.
Pretty much nobody but native New Orleanians get ‘New Orleans’ right.
It’s not New or-LEANS, and it’s not N’awlins. It’s also important to understand that the true New Orleans accent is not a southern accent, and it’s not a cajun accent, but it has its own unusual accent that, oddly enough, is closer to a Brooklyn accent than any other.
The right way to pronounce the city name is ‘new OR-lins’, with the ‘R’ sound subdued like a Brooklyner. The ‘new’ flows cleanly into the ‘OR’ sound.
Shouldn’t it be New Or-lee-auhn? 
Quincy, MA
Locals: ZWIN-zee
Others: Zwin-ce
Bogota, NJ
Locals: Ba-go-da
Others: BO-ga-ta
In Cornwall, in the UK:
St Austell: Pronounced as you’d expect everywhere except Cornwall, where they pronounce it “Snozzel”.
Launceston is usually pronounced “Lornston” or similar, but the locals pronounce it “Larnsten”. Generally with a piratical “arrrr” in the middle.
Honolulu is Ho-no-lu-lu, not Ha-na-lu-lu. When you live there, they mercilessly rag you if you pronounce it the latter like some tourist.
Although Thais call Bangkok as Krung Thep, they do know “Bangkok” but pronounce it Bahng-gawk.
Some locals say it that way, not all, 
Residents of Newark, DE always get a chuckle out of me by insisting that it be pronounced as two words as New-ark.
They won’t hesitate to correct you, either. I’m sure they do it to distinguish their city from Newark, NJ.
Somebody will correct me if I’m wrong, but it seems to me that most locals pronounce the middle vowel of Chicago like “aw” but most non-locals pronounce it like “ah.” Shi-KAW-go locally vs. Shi-KAH-go elsewhere.
A lot of locals seem to pronounce Toronto with two syllables, as if it were spelled Tronno.
Maryville, TN
Normal people - Mary-ville
Locals - Mahr-ville
It’s not just a southern accent. They will correct you if you say Mary.
I spent an evening talking to some Canadians that kept mentioning their home. Some area called ‘Noo Flun’. It took me 3 hours or so before I realised that they probably meant ‘new foundland’.
It’s all one word: Newfoundland. Always struck me as one of the worst place names ever.
Bowie, MD
Locals: Boo-wee
Others: Boh-wee (as in David Bowie)
Friends from there have always told me “new-OR-lins,” but my favorite band is from there and they always say “new-OR-lee-uns” (they sing about New Orleans a lot). Is there a pronunciation divide among residents?
Spokane, WA is Spo-CANE. It’s Spo-CAN
Yakima is not Yakeema.
Is this pronunciation in a song, or is that how they say it when they talk? Because it’s often different in song, depending on the needs for rhymes/rhythm/syllables/etc.
What band, by the way?
I’ve always heard that the rules are thrown out when using it in a song. You often hear new-or-leens.
Do you know what it means
to miss New Orleeens.