I've had good luck with planning a couple trips just by stringing together state park campgrounds in the parts of the state I want to visit. You can also think about integrating Amtrak into your trip if that is helpful. One tip given to me by a state park trooper: VT state park campgrounds state on their site that you need to purchase a minimum of two nights for every camping reservation, though there is an exemption for those traveling by bike or foot. However, if you want to do that, you have to make your reservation via phone instead of the site. Saves you a bunch of money.

If you're up for it physically, I'd also recommend attacking one of the famous "gaps" in the middle of the state.