What's the noun for approachableness? Here's the word you're looking for.
approach
The act of drawing near; a coming or advancing near.
An access, or opportunity of drawing near.
(plural) Movements to gain favor; advances.
A way, passage, or avenue by which a place or buildings can be approached; an access.
A manner in which a problem is solved or policy is made.
(used only in the plural, fortification) The advanced works, trenches, or covered roads made by besiegers in their advances toward a fortress or military post.