Word, expression or idiom for looking at nothing in particular

Solution 1:

to look/stare into space is close to your description:

• to look in front of you for a long time without seeing the things that are there because you are thinking about something else:

  • He sat quietly for a while, staring into space.

MacMillan Dictionary

Solution 2:

How about zone out?

M-W:

zone out: to become oblivious to one's surroundings especially in order to relax

It's applicability extends beyond relaxing. One gets lost in one's own thoughts in many other contexts, during a conversation or at a meeting.

Solution 3:

You could also use the thousand-yard stare

a vacant or unfocused gaze into the distance, seen as characteristic of a war-weary or traumatized soldier