Not having your own transportation in the US is hard--let alone trying to ski without it.
Unless you are eating out a lot, willing to make long walks to just about anything, and okay with being very limited in where you can go I would suggest getting a car, at least for part of that trip. I do realize a 2-3 month rental would be super expensive, and not 100% needed every day.
Nothing on the East Coast would be efficient for you, and even most places out west. Things are just so darn spread out.
Summit County has a bus system that connects Copper, Breck, and Keystone. I have extended family living in Breck that use it nearby their house. The schedule is not extensive however, and very much geared towards getting from hotels to skiing I think.
Aspen may have a bus system between Aspen and Snowmass.
SLC has some public transportation, and from what I have read could be you best general bet.
You may also want to find an area that has Zip Car rental service to get groceries, or at least a car rental spot nearby.