You can use Array.isArray to check for arrays. Then typeof obj == 'string', and typeof obj == 'object'.
var s = 'a string', a = [], o = {}, i = 5;
function getType(p) {
if (Array.isArray(p)) return 'array';
else if (typeof p == 'string') return 'string';
else if (p != null && typeof p == 'object') return 'object';
else return 'other';
}
console.log("'s' is " + getType(s));
console.log("'a' is " + getType(a));
console.log("'o' is " + getType(o));
console.log("'i' is " + getType(i));
's' is string
'a' is array
'o' is object
'i' is other