Redpill has a point- you should walk the neighborhoods that interest you. I’d say the whole of Newburgh is a block by block case. You are interested in walkability. What will you have to walk past to get to where you want to go? You’ll have to do trial and error walking the streets to see if you are comfortable.
The entire city of Newburgh is walkable. The question is, what do you want to walk to? For me personally, the most desirable spots to walk to are along Liberty Street near WHQ, Lower Broadway, and the waterfront (this is where you can catch the ferry to MetroNorth). If you were to move in the Heights you could surely walk to all of these locations, but again, you might have to walk past areas that you might not feel comfortable. Same goes for MGL. Another option is biking. Overall though, it sounds like you want to be near WHQ and the immediate streets that radiate out from it – Ann, Washington, Spring, East Parmenter, South William is coming along, and also the southern block of Grand. Hope it works out for you!