The nearest airport from Sikkim is Bagdogra airport. There are no direct flights from Pune to Bagdogra Airport. You can easily book connecting flights or travel to Mumbai and take a direct flight from Mumbai to Bagdogra. From Bagdogra airport it takes around 5 hours to reach Gangtok by road. If you are planning a trip to Sikkim, you can read my blog which has all the details. https://tripoto.page.link/eWpLWUCyFDMNRDXE7