Yes, you can choose to abandon a quest at any time. However, if you decide to abandon a quest, you will not have the opportunity to replace it with another quest. You'll need to wait until the following day for another quest to be offered to you. You will not miss out on the final prize offered for visiting each day. If you abandon a quest on the final day of the event, you will not have the opportunity to complete a quest until a quest is randomly offered to you through a regular Random Event.