I love the point-(the-car-)and-shoot idea -- some of my favorite vacations were done that way. But if you want to see "beautiful natural places before they change or disappear", I think you'll have to do more planning -- unless you can pick a highway like I-90 that passes through or close to several scenic areas.
Maybe you could narrow it down to an area of the country/world of which you'd like to see more -- or have never ever seen? And, if you can include some non-U.S. destinations, could currency exchange or the destination's local economy have a bearing in how long you could stay or how much you'd have to spend?