I went to North Sikkim two years back with my family. We took a flight from Delhi to Bagdogra. From there we took a taxi to Sikkim. In the route we watched various temples and monasteries of monks. There are a number of ancient Monasteries. They were also having ancient things like books which are approx two thousands years old. The beauty of the valleys and mountains is very awesome. The temperature is moderate in day and cold at night so travel accordingly. The route is very safe, the roads are made wide from before but still make sure your driver is experienced.
I visited in the month of May so the climate was very suitable and the rainfall was less. Make sure you make your trip here when there is less rainfall as you may struck here and rainfall also causes landsliding problems.
We stayed in Gangtok for two days. The local sight-seeing was beautiful and the nature of the public there is so calm and patience. The best thing I like about Gangtok is Its market. It is like I am in Delhi, its so developed. Another best part of Gangtok is that it is pollution free and tobacco free too, You will not find poly bags and there is less land pollution.
Then we went to visit Nathu la pass. It is the border of Sikkim and Tibet. We started our trip in early morning and reaches there at 12 noon. The beauty of mountains and specially the lakes are like heaven. The height is nearly about 14000 feet and covered with deep snow. Here you can see the army of China.
I fully recommend to travel to North Sikkim those who likes the adventure, are not too old and not afraid of height.