Is it more correct to write 金沢市 or just 金沢? (Kanazawa city or just Kanazawa
The same question goes for 広島市 or 京都市 (Hiroshima or Kyoto)
thank you!
Depends.
For referring to municipal division, writing your address and other official business, or to disambiguate prefecture and city of the same name, usually with 市.
For everyday communication (also including e.g. JR train stations), usually without 市.
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Yep, definitely depends on context.
Unless the 市 happens to be part of the name of the station, for example 山梨市駅 located in 山梨市 which is located in 山梨県. 
Not entirely sure why you’re bringing up JR specifically, though.
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Simple, think about contexts in which people might wonder what “correct” is. The way cities are called by a nation-wide transport company is a decent contender for being relevant.
But you are extremely welcome to bring in some other examples too to paint a fuller picture.
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Japan has over a hundred passenger rail companies. If I start listing them, we’ll be here all day. 
I mean I’m sure there are other reasons, but it’s sometimes used for disambiguation between the different scopes the city name is referring to.
Like, people will often say something like, “I used to live in New York State” - the “state” is technically not necessary but they’re specifying NOT New York City. “We’ll meet up at 広島駅” is different from 広島市, is different from 広島県 and sometimes it matters which you mean.
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the context is very simple. A series of posters with a photograph and the name of the city written on it