Where is Mt. J.Q. Adams, you ask? Why, it exists in the mind of a man long dead, one Mr. Hall J. Kelley.
He was a proponent of American settlement of Oregon way back in the early 1800s. In 1835, he proposed renaming the big volcanos of "Oregon and High California" to honor our presidents.
I guess he never traveled further north than Portland, since he starts with Mt. St. Helens being renamed Mt. Washington.
Here's a list of his proposal from a USGS webpage:
Territory of Oregon and High California, by Hall J. Kelley, 1834-35 -- map courtesy College of the Siskiyous Online Map Collection, 2002
"Mt. Washington" (Mount St. Helens)
"Mt. Adams (Mount Hood)
"Mt. Jefferson (Mount Jefferson)
"Mt. Madison" (Three Sisters)
"Mt. Monroe" (Diamond Peak)
"Mt. J. Q. Adams" (Mount McLoughlin)
"Mt. Jackson" (Mount Shasta)
So back to the original question: Where is Mt. J.Q. Adams? Well, where is Mt. McLoughlin, for that matter? Answer: very southern Oregon. It's a cone similar in shape to Mt. Hood.
Here's
a map of the Cascade volcanos.
Andrew Jackson was president at the time of this proposal. If the government accepted this proposal, we couldn't have continued much further southward with new presidents. Lassen Peak would have been Mt. Van Buren, and then what?
Note also that Mt. Adams hadn't been discovered by the Americans at this point. A map-maker who liked Kelly's idea misplaced Mt. Hood on the wrong side of the Columbia River, accidentally locating it almost exactly where another volcano existed. When it was discovered a few years later, the name stuck.
A volcanic Mt. Washington now exists in Oregon, between Mt. Jefferson and Three Sisters, which would be completely out of order.
Maybe we should start back at the northern border for new presidents:
Mt. Baker would be Mt. Harrison.
Glacier Peak would be Mt. Tyler.
Mt. Rainier would be Mt. Polk.
Mt. Adams (or Mt. Hood) would be Mt. Taylor.
Three-Fingered Jack would be Mt. Fillmore.
Mt. Washington would be Mt. Pierce.
Broken Top would be Mt. Buchanan.
Mt. Bachelor would be Mt. Lincoln.
Mt. Bailey would be Mt. Johnson.
Mt. Thielsen would be Mt. Grant.
Or not.