So what happens when i finish exploring a location that has an objective, and i wish NOT to claim it?
Does it go back in the staging area? If so, does it automatically go to an enemy or another location there? or does the next card from the encounter deck attach to the objective?
From official FAQ 1.2 (should answer to all your questions)
(1.17) Unclaimed Objectives
An unclaimed objective is one that is not currently
claimed and under the control of a player. An
unclaimed objective can be guarded or unguarded.
A guarded objective is treated like an attachment if
guarded by an enemy or location, and remains attached
to that card until it leaves play, at which point it will
return to the staging area. Any unclaimed objective
in the staging area that is not attached to a card is
considered to be unguarded. If an objective is claimed
at one point, and then returns to the staging area, it
regains the status of unclaimed