In Uttrakhand you visit Nainital, Ranikhet, kedarnath and many places are there. When you go you will find automatically. just wanna say start from Nainital because in November or December months you will see ice fall in nainital and weather will be clear so you can enjoy everything like himalaya darshan and many more things you gotta when you will be there.. Thank you very much. :)
If you want mountains and lakes together then nainital and bhimtal is awesome place, tehri lake is also a great destination with floting cottages ,motor boats, is also a emerging destination for tourist . if you are adventure freak then rishikesh is great place(rafting,bunjee jumping,air safari ) uttrakhand is a trekking hub also but there are only few winter treks operating after some days where you can witness lots of snow.
Religious places: kedarnath badrinath tungnath aadibadri yamnotri gangotru (confirm the timings as they might be closed)
scenic: chopta chakrata Mana (last village of India) auli dhanaulti mukteshwar kasauni binsar
Uttarakhand hosts many range of places to visit like the spiritual places of rishikesh, and kedarnath, advaita ashram mayavati, to the romantic hill stations like nainital, Ranikhet, kausani, almora, etc. you can choose according to your travel preferences