6. Youthful Curiosity
As Peter Davison was the youngest Doctor at the time (and second youngest overall, after Matt Smith), it was almost obvious he would have the traits of someone in their youth, regardless of his true age. In this incarnation, he displayed a curiosity not seen by many other versions of the Doctor which allowed him the freedom of exploration without the burden of needing a mission to do so, which has been an underlying problem with the NuWho Doctors (the Ninth was searching for the cause of Bad Wolf, Tenth was trying to avoid the ominous "four knocks" and the Eleventh... well, he had a few, including searching for Amy Pond, avoiding Trenzalore, etc).
Peter Davison's Doctor had none of those concerns which is generally a breath of fresh air. In fact, the "worst" thing that ever happened to him (besides his regeneration, of course) was that he became Lord President of Gallifrey. Speaking of which...