North Sikkim package may be 2D/1N or 3d/2N. I would suggest to go for 3D/2N tour.
This is best part of the trip.
The trip will start at 9-10am from Gangtok. You will arrive at Lachen at around 7-9 PM passing through Dikchu(32 KM), Mangan(64 KM), Naga waterfalls(82KM), Chungthang(100Km).
Normally, the vehicle doesn't stop at Dikchu, but you can ask your driver to stop for a few minutes. Dikchu is a small village in North Sikkim district at the confluence of Teesta and Dikchu river. Here you can buy the snacks, booze, (Don't buy the local bear because of poor quality) cold drinks etc. Because from here the rates of everything will increase (eg.Rs10 snacks packet will be of Rs15). I personally felt the very much positive energy there. If u feel the same please let me know so I can become a little bit sure that this was not just a hunch. You must try momos there.
Mangan is headquarter of North Sikkim district. It will take 3 hours from Gangtok to reach Mangan. In sharing cabs, the cab stops here only for check post. Mangan is also developing into a tourist hotspot because of the breath-taking view of the Kanchenjunga range it provides. This town has a hot water spring which is a popular tourist destination and the Labrang monastery which is located near Mangan is also a place worth visiting. During your trip to Mangan, you can also go for trekking. One main famous trek is Green Lachen Lake Trek(3 Days trek) which provides a view of Mt. Siniolchu.
There are various waterfalls along the highway. Naga waterfall( a multilayered waterfall ) is one of them. It is worth to stop for a stretch and take some pictures. After that, the sharing cab will go non stop because the driver will say it is going to be late.
Chungthang is a small town in north Sikkim district. It will take 6 hours from Gangtok to here. Actually, from here bifurcation starts, One road on the left goes to Lachen(26 KM)and the other road on the right side goes to Lachung( 22KM). The Teesta river is formed here by joining of Lachen and Lachung river.
You will arrive at Lachen at around 7-9 pm. Lachen is just a point to stay( not a tourist point). Now relax and take some rest in your room then go for dinner which will be provided in the hotel's dining room. If you are not feeling tired then drink some booze (take it from Gangtok or Dikchu )and enjoy music (for that carry a Bluetooth speaker with you). You will have an awesome feeling (no words to describe). Go to sleep early as next morning you have to wake up at 3 AM.