Elise cannot be found for quite a while if you choose to save her. You may find her if you choose to complete the quest 'Kidnapped'.
This quest begins in Bowerstone Industrial outside of the Orphanage. A man will ask you to find his fiancee, who has been kidnapped. After accepting the quest, you will find that the kidnapped girl is none other than Elise. At the end of the quest, you may choose to have Elise stay with the man or break up with him for you. If you choose to make Elise break up with him, she will tell you to come back in a few days, and a quest should pop up( quest named: A Lost Romance, Located In Bowerstone Industrials.