I recommend using the built-in functions from jQuery or lodash/Underscore. They're simpler to use and easier to read.
Either function will handle the case DRAX mentioned... that is, they both check if (A) the variable is a string literal or (B) it's an instance of the String object. In either case, these functions correctly identify the value as being a string.
lodash / Underscore.js
if(_.isString(myVar))
//it's a string
else
//it's something else
jQuery
if($.type(myVar) === "string")
//it's a string
else
//it's something else
See lodash Documentation for _.isString() for more details.
See jQuery Documentation for $.type() for more details.