I think what makes a place live on in our memories is the new things we experienced there. For example, in “The Queen Bodega” she talks about how the Bronx lives on in her memories because that's where she had her first boyfriend and her first kiss. She also states that she remembers the Bronx because that was where she was trying to fit in with the Dominican kids.
I feel like you can also get memories of how you feel at the moment you're doing something. Another example is in the song “Memories” it says “there's a time that I remember, when I did not know there was no pain”. In this sentence he is saying he remembers when life was good and he was happy, and now that lives on in his memories.