Darjeeling and Sikkim are adjacent, though it takes time to travel from one to another. Say for an example Darjeeling city to Gangtok is about 6/7 hours of drive. Also for Non Indian’s/foreigners, entry to Sikkim is either via Melli (for West Sikkim) or via Rangpo (for Gangtok and North/East Sikkim).
You have total 7 days assuming an afternoon/evening flight on 1st Nov from Bagdogra. Touching Sikkim and Darjeeling both can be tedious and tiring with a significant portion travelling in car.
We would like to understand more here about your trip preferences. Is including both Sikkim and Darjeeling your priority? If only one, then which one? How much important is the hiking part to you?
E.g if you decide only to stay inside Darjeeling district (West Bengal) then a Singalila Ridge i.e. Sandakphu trek along with Darjeeling city will be a suitable option. This will give a feel of complete hiking experience with a night or two relaxing in Darjeeling city or around.
In case of only Sikkim option, we would suggest couple of days in Gangtok area first (we process your Trekking Permit/PAP meantime inside Sikkim) then moving to West Sikkim and try Barsey Rhododendron Sanctuary trek. This is a short and fairly easy trek in contrary to Sandakphu.
It’s really nice to see the details of your planning, much appreciated. It helps in our understanding too.
As now you have more days, your proposed itinerary looks more complete. As I understand it, here are my thoughts:
1) Day 1 Chitrey: This is a small hamlet with few houses, one homestay/lodge and a monastery. Set up is very basic rooms, triple quad sharing type, more like 2+1+ 1/2+1 type of bedding. 3 Km below Chitrey is a small town on India/Nepal border called Maneybhanjung. Here we have arrangements with a local homestay, which is clean with attached toilet and running hot water. They serve home food which I felt tasty. Also the Sandakphu road from Maneybhanjung via Chitrey is closed by 2 pm (you have to reach Maneybhanjung by 1 pm, as there are foreigner permit formalities here). It takes around ~ 4 hours from Bagdogra to Maneybhanjung with a lunch break at Mirik town. Next day you can start trekking from Maneybhanjung in the morning to Chitrey and then to Tumling as per itinerary. Many Europeans travellers stay first night at Darjeeling, then next day morning drive an hour ~ 30 Km to Maneybhanjung and trek to Tumling with us. Here the climb from Maneybhanjung to Tumling becomes moderate as there is a steep uphill till Chitrey, which is 3 Km additional than our standard itinerary.
2) Pelling is a nice tourist town, with great views of Kanchenjunga. I am hopeful that you will get ample views of the mountains already in your trek. You may consider your Sikkim base at Yuksom, 40 Km further from Pelling. You can still visit Pemayangtse monastery, Rabdantse ruins, Khechepalri lake, Kanchenjunga falls etc, on your way, or short detours. At Yuksom you will get good hotels as well as nice homestay accommodations. There are places in and around Yuksom, the first capital of Sikkim. A lake, monasteries, Coronation site. On top of that, a nice 3/4 hours hiking to Dubdi monastery, Sikkim’s oldest. Holiest of these monasteries the one at Tashiding is 25 Km away one a different road than Pelling. To summarise Yuksom should give you more “Sikkim flavour” than touristy Pelling. Here you will get some idea about Yuksom and around: