Have you ever made a Pilgrimage, formally or casually, to a place associated with someone you admired?
I had a day to kill in Pittsburgh, so I drove down to Donora, and asked at the library, and went to see the house where Stan Musial grew up. I also once worked in the hometown of jazz great Bunny Berigan, and went to see his grave in the town cemetery. I think those are the only times I ever actually inconvenienced myself to do something like that.
I assume standard stuff – like Mt Vernon, or Gettysburg Battlefield, or Napolean’s Tomb – don’t count? How about a visit to the Biggest Ball of Twine in Minnesota? (The kids were hepped up on the Al Yankovic song.)
We’ve also made a special trip to Hannibal, MO, to see the Mark Twain birthplace and related.
I met WordMan at the C.F. Martin guitar factory in Nazareth, PA last summer. That (going to the Martin factory, not seeing WordMan :D) felt like a pilgrimage.
I took a tour of H.L. Mencken’s house in Baltimore back when that was still possible. It was pretty cool to see his desk in the room where he wrote.
In Jamaica I visited Bob Marley’s home/museum/sanctuary.
A few years ago I went to Galileo’s exhibit at the Philadelphia Museum of Art. It was in no way a pilgrimage because astronomy is just a casual interest. But then I found myself standing just a couple of feet from one of the first telescopes built by Galileo and I was surprised to find myself moved by it’s significance. I had to actually drag myself away from it after a little while. I’ve stood in front of great works of art by Renoir and the like; Never felt anything remotely similar, before or since.
Does going to Disney World count?
I’m not the OP, but I would guess it would count if you went to e.g. Mt Vernon primarily due to a specific great respect or admiration for George Washington or some other member of his family. If you went out of a general interest in US history, it wouldn’t count.
Did you enter the deep freeze and view Walt?
It took a large number of years but eventually I did the entire “Frances Slocum Trail” from near her home, through the park that was named for her, through New York, and all the way to “Deaf Man’s Village” in Indiana.
I also like to visit French Azilum as much as possible.
While driving through Tupelo, or Memphis, or wherever, I took a detour and saw Elvis’ birthplace.
While in Arkansas, I went to see Sam Walton’s home, and then, still Arkansas, I went to what was the Daisy BB Company, or whatever it is called.
Also, went to Dealey Plaza.
When I was younger I tried to go to the site of every battle in the former Yugoslavia one of my aunts had been in. It was very moving. I met people who remembered the battles and told me more stories about the war. In some places there were still bullet holes in the walls.
I visited Ernest Hemingway’s grave in Ketchum, Idaho. That was a choice I specifically made and had to put effort into doing it. I wanted to go because I fancied myself something of a Hemingway scholar at the time.
On the same trip I visited the eternal resting place of Dwight and Mamie Eisenhower, but that was a case of Q:What is there to do in Abilene? A:Racing Greyhound Hall of Fame, and Eisenhower Library. Okay, I guess we’ll do that.
Cemeteries are big business where I’m from. We’re tripping over celebrities and I’ve visited a lot of their graves but more as a cemetery tourist than “I have to stand at the feet of Glenn Miller.” I did make and actual plan and visited Judy Garland’s grave, a couple towns away. That was really accompanying a friend on her pilgrimage 'cause I had a car and she didn’t.
Many years ago, a friend and I visited the grave of Field Marshal Erwin Rommel. It’s in the little town of Herrlingen near Ulm.
A few years ago when we traveled up the east coast I made it a point to go to Stephen King’s house. My husband took a picture of me standing by the gate. I’m sure people do it all the time and Steve’s a good guy, but I was irrationally worried he was going to stick his head out the window and holler at me to get away from there. 
I made a pilgrimage to Billy the Kid’s grave. Everyone in New Mexico is required to go at least once.
I’ve been to Pine Mountain in KY a couple times and my mother has been there several times for personal reasons. A confederate ancestor was captured by the Yankees up there. (Also, it’s a nice place with a great view.)
Wife dragged me to Johnny Cash’s house and grave. Buried right across the street from a Home Depot, and some asshole (was it Berry Gibb?) burned down the house since.
I want to go to Maranello.
I’ve been to Tolstoy’s grave and picked a blade of grass off it that I still have. I also have been to Upton Sinclair’s grave, but that’s about a block from my house.
When I was in Britain I went to several Beatle and Who-related spots: Abbey Road, Liverpool, Leeds, The Marquee Club, and Brighton.
Many times. There’s an annual one in Australia on the feast of Christ the King (the last Sunday in October) where we spend three days walking from the cathedral in Ballarat to the cathedral in Bendigo. It’s modelled on the famous Paris-Chartres pilgrimage.