Pack some nice homemade food, cause this isn't a short trip !
There are direct trains but no direct flights for this journey. Chennai (Tamil Nadu) to Varanasi (Uttar Pradesh) distance is 1860 km and you can get there by flight + flight in just over 6 hours and 57 minutes or by train fares starting from ₹ 633.
Beautiful weather for sightseeing and other outdoor activity.