It's really the best time to visit Darjeeling and Sikkim which you have chosen. Solo tours are no less interesting. You can get cabs from NJP Railway Station for both Darjeeling and Gangtok and the same from Bagdogra Airport. If you wish for the Toy Train, then you need to enquire and book your tickets for it at the earliest.
On the way to Darjeeling you'll find Sukna, Rongtong, Kalimpong and Sonada. Treat to watch. And on the way to Gangtok, you can find Sevoke, Kurseong etc places.
Hope you pack your bags well 😉