I think the best you are going to do is the word reminiscence.
A reminiscence could be pleasant and precious, though not necessarily. In its favor is that the person who is reminiscing is choosing to remember something precious, whereas a person with an unpleasant memory might choose to suppress or repress it (though I'm sure there are people who hold onto bad memories and re-live them, so to speak, again and again masochistically).
Not in its favor is that reminiscence is often accompanied by a descriptor. Some examples:
a pleasant reminiscence
a nostalgic reminiscence
my favorite reminiscence
a shared reminiscence