This is one book that I read recently just for sheer pleasure and, further, just to see what "real teens" were reading and were "into." I also wanted to make sure I read it before I saw the movie. The book blew the movie out of the water.
That said, your question is interesting because it asks about some "ideas of value." What a different way to talk about theme! I will give you one short quotation, two tiny quotations, and one theme which will provide a perfect answer to your question.
Pain demands to be felt.
This is an incredibly important line spoken by Augustus Waters at many points in the book. It is later echoed by Hazel Grace in some of the most moving scenes of the book. Green gives a perfect example of this quotation in the character of Issac, now blind due to a rare eye cancer and a recent operation, who was just dumped by his girlfriend for that particular shallow reason. Issac cries and yells and throws things in despair. Augustus Waters suggests that all three of them (Issac, Hazel, and Augustus himself) pay a visit to this ex-girlfriend and pull a traditional house "egging." Even though blind, Issac succeeds in making his mark along with his two friends.
Another idea that stands out is actually introduced by this minor character of Issac who has this mantra with his (now ex) girlfriend of "always." It is their word of devotion: their declaration of love. It is also an irony in that the relationship doesn't last. As Hazel Grace and Augustus become more involved, they create their own word (on accident) that sums their relationship into a word of devotion, or a declaration of love, as well: "okay."
Finally, one can't speak about The Fault in our Stars without talking about sacrifice. Both Hazel Grace and Augustus Waters are terminal cancer patients. The "surprise" of the book is that Augustus has less time to live than Hazel. As cancer patients, they are always talking about "cancer perks," which are things afforded to you when you have this condition. One of the most significant "cancer perks" is their "wish." This is the vacation each child with terminal cancer is provided from the Make a Wish Foundation. Augustus Waters is disgusted to learn, early in the book, that Hazel Grace "wasted" her wish on Disney World. (Her argument is that, at the time, she was young and stupid.) The clincher here is that Augustus Waters sacrifices his wish to take Hazel Grace to the Netherlands in order to meet her favorite author. This is done out of pure love. In my opinion, this is the most altruistic and compassionate thing a person can possibly do: sacrifice one's dying wish for the person one loves most in the world.
In conclusion, I want to say that last night in the midst of our substance abuse counseling group, the phrase "pain demands to be felt" was the main topic of discussion. Five words that apply to everyone today, not just teens.