I read this book in 2014-2015 about this girl that was raised in a rich family, or royal family. She lives in the "new" city above a post apocalyptic city where the criminals and poor live. I think that one of the ways to get into the upper city was to ride a gondola type thing.
She ventures into the lower city were she meets a boy and they become friends and eventually fall in love. I remember her getting caught by her family and her memories are erased(?) The book was post-apocalyptic with new technology in the upper city.
I think I might be mixing up two different books, but I could swear that this was just one book.