Obviously, some states will be more challenging than others—I’m looking at you, Florida— but I was fortunate to have the ability and opportunity to reach the highest point in Washington State on several occasions back in the eighties when I was with the local mountaineering club.
No, but I’ve gotten pretty drunk a few times. 
I can’t say I’ve been precisely at the highest point in Florida, which is Britton Hill, at a whopping 345 feet above sea level, but I’ve been in the general area. Got light-headed because the oxygen is so much lighter up there. 
Texas: Guadalupe Peak a couple of times, geology field trip, guy’s vacation.
Oklahoma: Black Mesa, geo field trip.
Colorado: 2nd highest, Mt. Massive, Outward Bound.
Nope, it’s pretty out of the way…but just for a laugh, take a look at Mount Sunflower!
I’ve been in the general area, but I’ve never been to Eagle Mountain in Minnesota. It is beautiful up there - been to the Boundary Waters Canoe Area a few times.
Used to go up Clingman’s Dome in East TN, usually after a night of getting wasted, to catch the sunrise.
Ontario’s is pretty inaccessible.
I have been on Mt. Whitney but not atop it. It is the highest peak in the Lower 48.
Yes, Greylock in the Berkshires. I’ve also been to the the highpoints in NY, ME, VT, and NY. I have friends who have done or are pursuing the 50 state highpoints but it was never a big draw for me. Some even go so far as hitting the highpoints of each county in a state.
Another Washingtonian here. Haven’t been to the top of Mount Rainier but have made it as high as Sunrise.
I’ve been to the high point in New Jersey, located in (appropriately enough) High Point State Park.
Was just going to post this. Missed it by that much.
Likewise. I’ve hiked partially up it, but pretty sure I didn’t come anywhere close to the peak.
Yes, top of Mt. Bimberi during an Outward Bound hike. Also #2 and 3 which are neighboring peaks.
Given recent changes in state law, I would expect that the highest place in Washington State is either a club or a college campus.
For years the hardest state highpoint to reach was in RI. There was a private landowner who didn’t allow access across his land to the HP (which was on Brown University land). He prevented folks from legally making the short walk to Jerimoth Hill except on one day per year. That’s no longer a major obstacle as the property has changed hands.
That would be the highest state in your point.
Yup. In Georgia that would be Brasstown Bald at 4,784 feet above sea level.
Made it to the top of Mt. Whitney once. My second attempt was unsuccessful due to inclement weather (on 9/11/2001).