I read a number of the comments about whether or not the natural or the man-made high point should be considered. To me, the HP Club recognition, scenic beauty, and convenience/inconvenience are all secondary issues. What is really at stake is the personal satisfaction of having completed the goal - however you interpret the goal - natural, man-made, or other. Most folks aren't going to challenge you if you say to made it to Charles Mound - and call it Illinois' High Point. Likewise the Sears Tower. But how do you feel? And if it is critical to you - visit both.
I concur with the sentiments of Joe Borondy - too many disparaging remarks about the Wuebbles and other private owners setting parameters for the visit. Thank heavens, these folks recognize the passion that we have for our "sport" - and have made some accommodations to allow us to visit - sometime, somehow.
I went to Charles Mound early Saturday morning on the first open weekend of 2015. The scenery was typical Midwestern, nothing special. But I met about a dozen folks in the course of that 2-mile round trip walk - all with the same passion as mine. A couple of these brief encounters have turned into friendships. That is part of the sport too. I met another person at the HP Convention last year - we climbed Granite together - and now we have had discussions of linking up for other high points.
My own parameters are to do the highest natural high point in each state - to the extent that is possible and recognizing that man-made alterations have removed or changed the "pristine" high point. In some cases, it simply isn't possible to know. There are a number of boulders (seemingly in their natural locations) on Mt Whitney - to my mind's eye - that might actually be California's highest point. Several appeared to me to be higher than the point where the geodesic marker was placed. Conversely, the little hut on top - whether higher or not - was not my object - I wasn't going to clamber onto the roof to make a point (and probably get arrested?). The tougher question to me are the cases such as Cheaha, Greylock, and Highpoint, where there are man-made structures on top of what is ostensibly the true high point. Obviously, the ground has been altered to constuct these buildings and towers. My personal fetish is to try to identify what appears to be - or might have been -the natural high point - and stand on or at least touch each of the reasonable candidates in the vicinity - and a few others just for good measure. I have listed what I deemed to be the most probable candidates in several of my trip reports on another site (peakbagger).
On a side note, I'm wondering if there is a comprehensive list of all of the (natural) high points that are on private property, and/or require special training, permits etc., or have limited times/access periods. I know about Charles Mound, and Kentucky's and Ohio's high points. I know you need a permit for Whitney (even though on public lands). I noted time-of-day restrictions for Jerimoth Hill. I think North Dakota's and Nebraska's high points are also on private property, and there have been occasional interruptions to access. It would be a real shame to drive halfway across the country for a high point - only to find that it isn't open, or that you need a permit that you didn't get before your trip.
David C Odenwalder