The answer to this question is at best debated, but for all intents and purposes is unknown. While the hippocampus and surrounding cortical regions are necessary for memory formation and consolidation, it is unclear if there is a specific location where memories are stored per se. Individuals with anterograde amnesia usually have damage to the hippocampus, and while they cannot form new memories, typically still have access to memories preceding injury/disease onset, which would suggest the hippocampus does not "store" memories.
The more likely way that memories are stored is that specific memories recruit specific populations of neurons which "code" a memory. The reinstatement or reactivation of those neurons in the specific pattern could potentially underlie the retrieval of a memory. Since neurons throughout the brain are involved in encoding and processing a stimulus - the visual cortex for what you see, the auditory for what you hear, and so forth - it is unlikely that there is any single region which stores memories.