I will be in NYC in the first week of January. Since I prefer sightseeing and not doing classical winter activities (ski etc), I wonder what sightseeing activities are available in winter in the Rocky Mountains?
Skip it this time
Unless you are interested in skiing, there are limited activities, and you will miss a lot.
All the major national parks (Rocky Mountain NP, Yellowstone, Grand Teton, Glacier etc) will be closed or partly closed. As will many hotels, most scenic roads/passes and so on. You can look for individual information about each park and its surroundings here.
The majority of this infrastructure will be closed until April (or later).