Torre grew up in the Flatbush area of Brooklyn at a time when three teams were still in New York. He lived about a half-hour's drive from Ebbets Field, home of the Dodgers, but inherited Giants roots from his family.
"Because of that, I automatically became a Giants fan," Torre said.
Torre played for the Braves in Milwaukee, and played for and managed them in Atlanta, played and managed with the Cardinals and Mets, and finished his on-field career in 2010 managing the once-hated Dodgers. But it was his Yankees years from 1996-2007 "that put me on the map," Torre said.
"It caught everybody's attention," said Torre, who won 1,173 of his 2,326 regular-season games, six American League pennants and four World Series titles while wearing pinstripes. "Not to mention the success we had."
Torre will be inducted into the Hall wearing a Yankees cap on July 27, along with fellow managers Bobby Cox and Tony La Russa. They'll be enshrined along with slugger Frank Thomas, and 300-game winners Tom Glavine and Greg Maddux, comprising a class for the ages.
"It's unbelievable, the whole thing couldn't happen again in a million years," Cox said after he toured the Hall with Maddux on Monday.
Torre said he's still trying to wrap himself around the whole experience. Accompanied by his wife, Ali, and a phalanx of video cameras, Torre toured the second-floor displays with a look of abandon. The Yankees have had so much success through the years that there's a display honoring their great teams of every era.
Want Yankees? There's the actual Yankee Stadium lockers used by Babe Ruth, Lou Gehrig and Mickey Mantle, replete with their famous uniform jerseys. Ruth, who has his very own nook, was among the first five players inducted into the Hall in 1936. His plaque hangs front and center with the four others -- Ty Cobb, Walter Johnson, Honus Wagner and Christy Mathewson. Two stalls down is the spot where Torre's bronze hardware will be hung with the five members of his class after they accept their plaques on the stage behind the Clark Sports Center this summer.
"They pointed out where my plaque will be," said Torre, who's last in alphabetical order in his class and will be located on the second row, third from the left. "Near Ruth? I said, 'Really?!' And the class I'm going in with, these are special people. The managers? I think when the three of us got in it made it that much sweeter. It was probably the first time we stopped lying to each other."
There were special moments along the way on Tuesday.
Gehrig took all his World Series and All-Star rings and melded them into a rare gold bracelet for his wife, Eleanor.
"That's a good idea," Ali said, looking at Torre.
Mantle's locker is part of a display honoring the Yankees teams that went to the World Series 13 times in 15 years from 1949-64, winning nine of them.
When Torre took over managing the Yankees, he was issued No. 6, Mantle's number as a rookie. Well aware of the honor, Torre called it "a good omen."
"My first Spring Training with the Braves was '61," Torre said. "Even though I was never a Yankees fan, I was catching, and Mantle stepped into the box. He was a giant of a man in my estimation. It was still what he represented and what they represented."
Torre didn't know then that his No. 6 would take a place a Yankees history. He wears his 1996 World Series ring "because it was the first and I just dreamed of being there." And there's a display honoring the four Fall Classics won by his Yankees in 1996 and 1998-2000. They lost in 2001 and '03.
On the display, there's a World Series celebration that was shared by the Core Four -- Derek Jeter, Andy Pettitte, Jorge Posada and Mariano Rivera. Three of them have retired, and Jeter is going into his final season.
"We were in six World Series together," Torre said. "But when they won it again in 2009, to see them all be such a big part of it, that was something special."
Torre wasn't a part of that team and he still regrets never having played in a World Series.
"I told Jeter, 'This isn't easy, pal,'" he said.
Any newcomer to the museum is ushered into a theater decked out like Chicago's old Comiskey Park and shown a 12-minute multimedia extravaganza called "The Baseball Experience." As in all of these tours, that was the first stop on Tuesday for the Torre party.
One of the slides is of Torre's Yankees lining up along the third-base line at Fenway Park, a huge American flag draped from the Green Monster, honoring a special occasion. Torre couldn't peg the moment -- Game 3 of the 2003 AL Championship Series.
It hardly mattered. This was Torre's day.
"It's a big thrill," Ali said. "He worked hard for it and deserves it. I'm very excited for him."