Good tree for climbing

Solution 1:

I (like many of the commenters) would call it a climbing tree.

Here are some examples of this expression in use:

TreesLouisville has access to this gorgeous Climbing Tree that is approximately 35 years old.
_{The Case for a Climbing Tree}

Qualities of a Great Climbing Tree

There were a few qualities that I wanted specifically for a climbing tree for our family.
_{3 of Our Favorite Trees For Climbing}

And it got me thinking about what makes a good climbing tree: [...]

Whether it’s from your resting spot or a perch high atop the canopy, a climbing tree should provide you with something wonderful to see.
_{Climbing Trees}

Solution 2:

An adjective you can use to describe a tree that can be climbed is climbable.

Solution 3:

Other adjectives are scalable, and ascendable, but these don't specifically refer to a tree, or necessarily to the ease of climbing one. You could try also describing it metaphorically as a ladder.