"Assuming that you are asking for treks in Winter", The best place for your first trip would be Kedarkantha Trek, Sankri (Dehradun) or Triund Trek, Mcleodganj, (Dharamshala). You can also visit Manali and explore treks like Kheerganga and Tosh.
Yes, you can visit Kasol in December. In case of heavy snowfall, the treks are closed but generally they are open. I am also planning for Kasol this December during the New Year. See you there..!!!
For a selection of the best trekking spots around Nashik, encompassing a range of natural landscapes and historical sites, you can explore detailed recommendations on trekking in Nashik: https://www.visitwander.com/trekking-places-near-nashik/
Small trek :-
1. Harishchandragad trek
2. Bakor trek
3. Kalsubai trek
4. Sondai trek Long treks :-
1. Brahmatal trek
2. Chadar trek
3. Kedarkantha trek
4. Valley of flowers trek
5. Har ki dun trek There are many more amazing you can contact to mountainsouls.in , Crazy peaks , Thy adventures , india hikes they arrange and amazing treks in affordable price.