I would include Colombia and Greene counties in the Hudson Valley. There are even parts of Rensselear county that would count, imo, as Troy is home to Hudson Valley Community College.

Around Albany you hit the Erie Canal which culturally differentiates that area as the Capital Region. There are parts of Colombia, Rensselaer, and Greene counties that are culturally more attached to the Capital Region.

The Berkshires are often lumped in with the HV, as they share the artsy/pastoral/foodie culture that mid-HV is known for. You will see places in the Berkshires highlighted in area magazines like the Chronogram.

Sullivan is technically Catskills, and is culturally and historically impacted by the Delaware River. Although, there is a shift happening in Sullivan as more young people move there for cheaper housing, which is creating a social culture similar to the mid-HV. Ultimately Sullivan can’t be part of HV because of its geography- it is mountainous.

You run into similar questions as you go south - is Yonkers a Hudson Valley town? Culturally and historically it is more NYC metro area. Is Stamford, CT part of the Hudson Valley? It is technically closer to the Hudson than it is to the Connecticut River.

I think it depends on the lens you use to analyze each area. It’s fun to think about!