Some of the things I have done to make the highpoints more interesting:
Alabama - Hiked from Cheaha Lake. I liked this short but steep hike.
Arkansas - I hiked RT from the visitor center, which I figured as 6 miles. There are some 5th class rock climbs on a cliff below Magazine Mtn, which could make a very interesting HP, but I didn't try to do this.
Georgia - I hiked from Jacks Gap, 5.5 miles RT. There are other (a little longer) trails to Brasstown as well.
Kentucky - I walked up the road from the state border.
Massachusetts - I hiked around 6 mi RT on the AT, starting north of the HP, to the west of Mt Williams.
Missouri - I hiked 26 miles RT from Johnson's Shut-Ins SP, along the Ozark trail. It was surprisingly crowded, although most people were doing the hike one-way with a car shuttle, this is still a respectable 13 miles on rocky trails. I don't know what the situation is post-accident.
New Hampshire - Hike from Pinkham Notch.
New Jersey - Hiked 5 mi or so RT on the AT, starting from the NE corner of the park.
North Carolina - Hike from Black Mountain campground. (11.2 mi RT, 3000+ ft elevation gain).
Pennsylvania - Hiked up Wolf Rock trail. I wanted to do a longer hike, but time and thunderstorms made me pick a shorter one, still better than drive-up.
South Carolina - 19 mile RT hike from Table Rock state park.
West Virginia - 20 mile or so RT backpack, starting on the Spring Ridge Trail on CR 29.
Wisconsin - 9 mile RT on the Timm's Hill trail, starting at the trailhead near Hultman road and Highway C. You could make this longer as well.
I should have walked from the state border on FL and RI, but time and weather considerations made me wimp out.