The journey from Gangtok to Belagavi covers roughly 2300 km. You must first reach NJP or Bagdogra. From NJP, you can take a long-distance train to Belagavi Junction. Flights from Bagdogra to Belagavi usually connect through Bangalore.
Total Distance: 2300 km by road, 1900 km air distance.
This is a very long journey; ensure you have a confirmed berth.
Bangalore is the most convenient hub for this connection.
October to March for pleasant weather.