Hmm. My favorite tree would be deciduous and climbable. So no conifers, or things like willows, palm trees (yes, people climb those, but not in the good way), or aspens. Oaks and maples are obvious answers. I have to admit, though, I don’t know trees very well.
OH WAIT. REDWOODS. HANDS DOWN.
Funny thing about that is that they’re not particularly climbable without gear, and they’re not deciduous.

