From Haridwar it takes 9 hours to reach Gangotri. You could take Rishikesh route, or devaprayag route. The journey is via the hills. June is a pleasant month to visit. The roads are good. From Haridwar Yamunotri is 6 hours drive. You could take Dehradun route. The roads are driving friendly. My advise would be from Haridwar you first travel to Yamunotri. Then from Yamunotri 7 hours away is Gangotri. Kindly see as per your travel plans.