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

Using JSON.parse() has some drawbacks:

1. JSON.parse(1234) or
2. JSON.parse(0) or
3. JSON.parse(false) or
4. JSON.parse(null)

all will return true.

function isJson(str) {
  try {
    JSON.parse(str);
  } catch (e) {
    return false;
  }  
  return true;
}

function testIsJson(value, expected) {
  console.log(`Expected: ${expected}, Actual: ${isJson(value)}`); 
}

// All of the following codes are expected to return false.
// But actually returns true.
testIsJson(1234, false);
testIsJson(0, false);
testIsJson(false, false);
testIsJson(null, false);

Code that handles false positives

So I rewrote code in this way:

function isJson(item) {
  let value = typeof item !== "string" ? JSON.stringify(item) : item;    
  try {
    value = JSON.parse(value);
  } catch (e) {
    return false;
  }
    
  return typeof value === "object" && value !== null;
}

Testing result:

function isJson(item) {
  let value = typeof item !== "string" ? JSON.stringify(item) : item;
  try {
    value = JSON.parse(value);
  } catch (e) {
    return false;
  }

  return typeof value === "object" && value !== null;
}

function testIsJson(value, expected) {
  console.log(`Expected: ${expected}, Actual: ${isJson(value)}`);
}

const validJson = { "foo": "bar" };
const notValidJson = '{ "foo": "bar" } invalid';

// expected: true
testIsJson(validJson, true);

// expected: false
testIsJson(1234, false);
testIsJson(0, false);
testIsJson(notValidJson, false);
testIsJson(false, false);
testIsJson(null, false);