Final answer:
The statement is false because the Three Broomsticks is not located in Diagon Alley, but Harry does learn about his fortune at Gringott's which is in Diagon Alley and run by goblins.
Step-by-step explanation:
You asked whether the statement about Gringott's Wizarding Bank in Diagon Alley is true, including details about it being run by goblins and that it's the place where Harry first learns of his inheritance from his parents, Lily and James Potter. The answer is False.
The Three Broomsticks, mentioned in the question, is not located in Diagon Alley, but in Hogsmeade Village. Gringotts is indeed the Wizarding Bank operated by goblins and it is where Harry discovers his family fortune, but the Three Broomsticks as a location is incorrectly associated with Diagon Alley in the question. It is essential to recognize these details when discussing the Harry Potter series in order to maintain accuracy regarding the setting and the events.