According to Wikipedia (that bastion of all knowledge on the Internet), there is in fact a "General American" accent. Regionally it corresponds to the American Midwest.

http://en.wikipedia.org/wiki/General_American

This does not, of course, imply that America's many regional dialects are "wrong" -- they're just different. And as Bruce correctly stated, you'll need to tune your ear. I'm a native speaker of American English, yet when I moved from one U.S. state to another I had to learn new ways to express myself. 

Television is a communication medium, so actors and broadcasters are trying to make themselves understood. At the risk of suggesting something even more vapid, try American "reality" TV shows. Sometimes the accents are so strong that even Americans need subtitles to understand what's being said! 

Real people mumble. Or stutter. Or talk very fast. Or mispronounce words. Or use slang. Any of these things can make it really hard to understand spoken English. So while you may find individuals who speak slowly and clearly in a relatively "unaccented" American English, you're not likely to find a whole community of people who do.

Sorry it's not easier! :)

Great Movie Musicals make for great Lesson Materials for learning English

These are not arranged in a special order, such as "best" or anything like that.

"Oliver!" 1968 http://www.imdb.com/title/tt0063385/

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"My Fair Lady!" 1964

http://www.imdb.com/title/tt0058385/?ref_=fn_al_tt_1

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"The Sound of Music" 1965

http://www.imdb.com/title/tt0059742/

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"The Music Man" 1962 http://www.imdb.com/title/tt0056262/?ref_=fn_al_tt_1

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"West Side Story" 1961 (based upon William Shakespeare's "Romeo and Juliet")

http://www.imdb.com/title/tt0055614/?ref_=fn_al_tt_1

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"Camelot" 1967 http://www.imdb.com/title/tt0061439/?ref_=fn_al_tt_2

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"State Fair" 1962 http://www.imdb.com/title/tt0056526/?ref_=fn_al_tt_1

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"The King and I" 1956 http://www.imdb.com/title/tt0049408/?ref_=fn_al_tt_1

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"Mary Poppins" 1964 http://www.imdb.com/title/tt0058331/?ref_=fn_al_tt_1

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   There is no such thing as a  "flawless"  American accent. 

Accents are not governed by any kind of regulation.

  There is no such thing as a standard accent.

You can use my Notebook Entries in which the lyrics to many songs in English,  and the links to videos offer you a full spectrum of English language  "accents".

Click on my picture, look for the "Notebook"  link, look for any song. 

   Develop your "ear" for English as spoken (or sung) by all the different kinds of people who speak English.   Also, you can benefit from wathing something besides the vapid TV programming.  Use Movies and especially the Musicals as follows:

.

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Throughout the English speaking world people have strong accents, and on TV actors are usually asked to use clear English that everyone can understand. In some cases, an actor will change their accent so that the audience will understand them. 

A good technique for learning the accent in the area you want to travel to, is to watch YouTube videos of people who come from the city or state you are interested in.