Hey ! don't miss out the naina peak trek, it's one of the most amazing place to visit. Chowli ki jhali gives the best sunset view , you're not gonna regret it. Tiffin Top trek is also amazing, it's a 4km trek for good 2hrs( two- way).
Check out Bhandardara, dist. Ahmednagar. It's an amazingly beautiful place. There's mountains all around. Bhandardara is situated in the midst of Sahyadri range. You must visit this place once at least. Check out The Land Of Wanderlust (TLOW) website..... https://thelandofwanderlust.com/
Both stations are there in the rishikesh itself ... book tickets to any of them and you may reach rishikesh ... you may get a local auto for 50-100 bucks to your hotel anywhere in rishikesh after that ... RKSH is near TRIVENI GHAT ... YNRK is a little afar !
Minimum 03 days you need,
One for Nathula and Baba Harbhajan Singh Mandir, War Memorial, Tsogmo Lake
Second day for Namchi and Hanuman Tonk/Mandir
Mall road and local sight seeing
Sikkim is itself best. but for traveling, gangtok to North sikkim or silery gaon to silk route. also ravangla namchi and a lot more beautiful hamlets to explore.
There is no official website to visit dudhsagar waterfall the only way is to reach entrypoint as early as possible so that you can avoid crowd during visit. second is go through train and then trek but i am not sure now it is allowed or not.