A special moment for Kobe Bryant's family ... when Vanessa and their children visited the NBA legend's exhibit at the Basketball Hall of Fame on Friday ... and it's a pretty emotional sight.

Bryant -- who is being inducted into the Hoops Hall on Saturday -- got his very own stand-alone tribute called "Kobe: A Basketball Life" in Springfield ... the first since Michael Jordan's exhibit in 2009.

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The 600-ft. display -- co-designed by Vanessa -- features incredible memorabilia from Bryant's career ... including a piece of the Lower Merion H.S. basketball court, the shoes from his 81-point game, game-worn jerseys, and a video screen showing his Oscar-winning short film, "Dear Basketball."