What are some things hazel grace does in the book to try to live life to the fullest?

When she forms her relationship with Gus, she begins (and yet pulls back from) that relationship because she wants to have a boyfriend.  However, the trip to Amsterdam, and all of the accompanying tourist "things" that she and Gus do show that she wants to get as much from each day as she can.  When Dr. Maria allows her to go on the trip, she emphasizes that Hazel Grace must live her life one day at a time.