So you know that (in your example) myString has your JSONed thing? Why not do:
var myVar = myString.substring(1, myString.length - 2);
If there's some other junk before or after your JSONed thing, I guess you could use the indexOf and lastIndexOf operations.
Also check out this question:
Regex to validate JSON
In response to the question in the comment:
//So let's say we have this string
example = '"[ { "title": "event1", "start": "NOW", } ]"'
//So our example string has quote literals around the bits we want
//indexOf gives us the index of the " itself, so we should add one
//to get the character immediately after the "
first_nonquote_character = example.indexOf('"') + 1
//lastIndexOf is fine as is, since substring doesn't include the character
//at the ending index
last_nonquote_character = example.lastIndexOf('"')
//So we can use the substring method of the string object and the
//indices we created to get what we want
string_we_want = example.substring(first_nonquote_character, last_nonquote_character)
//The value in string_we_want is
//[ { "title": "event1", "start": "NOW", } ]
Hope that helps. BTW if your JSON is actually coming back with the ', } ]"' at the end of it and that's not a typo, you'd probably want to do a string.replace(/, } ]"$/, '}]').