This is a very tough subject, as it would be much easier to say that different things happened in different places that made it more valuable and interesting all the while.
I'm of the opinion that English Film and Theater, was very important and influential between 1955 and 1965 and that it eventually took form in music. After this, I would say American Film was an influence. All of these can find threads in the wording and feelings, and even influence in the music itself.
I would think that France was pretty independent, but more open to weirdness than most folks around us. I don't think that a Heldon would have gotten released in London, because of its hardcore approach to music, which is something that Melody Maker and other magazines in London used to trash so well, including Tangerine Dream, and any bands that did not suit their definition of rock/pop/blues in music!
One other thread that runs through and is still ignored for the most part, is that the beginning of Pink Floyd and Soft Machine are tied to a house where many dignitaries lived for a while and shared more than just food and shelter. It also included various actors and actresses. And while there is a taboo about sex, there is no secret that one was gay, the other was picking up boys, and one other was making sure he scored on all the ladies and the wives! Both of these bands, and the following "Canterbury" design, was quite open musically in the style that this all came from. It's called "beat poetry" and folks like Robert Wyatt still live by it, regardless of how weird and different it is! Daevid Allen is the Ken Kesey of rock (progressive) music!
It's too easy for us to think that one is more influential than the other, but I sincerely do not think that anyone was more important in terms of lyrics, than Bob Dylan, and I find it strange that he was dis-regarded, specially when so many folks went out of their way to show this to the whole world. He is now accepted, but the influence is more on the lyrical side than musical side and it is "hidden", so to speak.
Of the less known variety, I would say Peter Hammill and Van der Graaf Generator, who are NOW, revered, but weren't in the early days, and I can tell you that for anyone around Southern California I have ever heard, I can count on one finger how many folks played his music, and he was my roomate at the time and continued to play his work even after I was gone. And I have a recording of one of the other guys on the station saying it was weird, but getting better about the album "Still Life" ... which kinda tells you how "still" their life was already centered around hit radio and top ten ... and this was a number one FM station!
The LA area, had its "big names", but of the "underground", I would say that the best influence of all was the "LA FREE PRESS" who was always given credit for being a troublemaker, but in the end, they were the ones that brought you history, when recognized a few years later! They were single handedly responsible for Frank Zappa's survival for some time until he finally hit the big time a bit later. We're talking 1968/1969 and 1970. Likewise the other wordsmiths at the time, would be the Firesign Theater in that area with the clever wording and well designed stuff satirising radio and television. They never got the credit they probably should have, but comedy is not appreciated in the "progressive" music circles, and The Goons were a huge influence on the Beatles, which you can not enjoy or appreciate until you listen to the 7 Beatles Christmas shows, and later them all having fun with Spike Milligan and Peter Sellers, in various affairs.
The Firesign Theater, in LA, if it can be said, became a sort of "symbol" for what was hip and cool and neat, and unffortunately the music for the housewives took over by the new owners of the FM stations that all sold out to the huge conglomerates, which made the study of "influence" a lot more difficult.
I can not, speak fluently the language of New York. So far, the only book I have read that is really with it, and more than clear about it's scene, is the one by Patti Smith, that you FINALLY, get the feeling that you were there! As much of the New York writers as I have read from the 1950's and 1960's, none of them are as valuable, as the bullsh*t that Andy Warhol became. And yet, you can look at Lou Reed, John Cale, and many other musicians as being influential in NY, but none of us has ever spent enough time finding out what all the bruhaha was about. In many ways, some movies tell an interesting story that we have a hard time seeing, and can not find (it's a movie?), but the similarities are still there. Hard living, etc etc.
Lastly, a lot of folks dismiss the strength and work of a lot of literature and how it affected things. If you EVER have a chance to see the film "The Trip" about Ken Kesey, you will see a very nice wonderful quote towards the end ... that is the most important part of it all and defines the difference between an "artist" and "everyone else".
It says (paraphrased) ... "... in the end, we were afraid, of experience, and learning! It wasn't the drugs."
And guess what most bands and crappy music ended up stuck on? Not the value, but the crap!