This thread must have gotten going originally when I was on vacation, because this is the first time I've seen it.
My most-frequently-climbed mountains are
Mount Monadnock, 14 times;
Mount Wachusett, 9 times;
Mount Watatic, 6 times; and
South Bubble, 5 times.
Of the 4000-footers, thrice apiece for Washington (although the third time the view was about ten feet, so that may not count as a view from the top), Liberty, Algonquin (the first time here the summit was socked in), Dix (ditto, but even more so), Panther, and Donaldson (third time was viewless).
As for the most-visited "place," I suppose Lake Placid isn't specific enough. Maybe the Adirondack Loj/ Van Hoevenberg Trail head parking lots? Eight hikes began there for my initial round of the 46, plus there were an additional two visits for climbs of Mount Jo and three more for second ascents of High Peaks, so that's at least 13 times I've begun a hike there.
There have been 12 trips up Route 25 to the several trailheads there. The first time didn't result in much of a hike (just to the pond on the left); the other ten led to climbs of High Peaks or Mount Adams.
It looks like I've been to Baxter State Park seven times, but the last time was actually two separate day trips, so that would make eight different times I've been to the Togue Pond gatehouse, not counting the day I broke a tooth while I was camping there and had to run into Millinocket to get it capped.