When using the "Fear" extra effect of the hallow spell, the spell says that affected creatures are frightened whilst in the spell's area.

With regards to the frightened condition: is the source of fear the point at which hallow was cast, or the whole area?

This matters for how it interacts with both parts of the frightened condition:

1. If the source of fear is the point at which the spell is cast, then
   affected creatures can move away from it and there might be ways to
   break line of sight within the hallowed area itself.


2. 
   

   If the source of the fear is the whole area, being inside the area
   means that the source of fear is in all directions from the affected
   creature. This would mean that the creature could not willingly move
   in any direction, as all directions would be closer to the source of
   fear.

   
   
   

   Alternatively, you could interpret it as you are always at the source of fear so you could freely move, as moving in any direction could not put you closer to the source of fear than you already are.

   
   
   

   In addition to the movement restriction/non-restriction (depending on your interpretation), the whole area being the source of fear would mean that you are always subject to the effect of being in line of sight of your source of fear whilst in the area.

   
   

What is the correct interpretation?

RAW: Unclear

As written, the Hallow spell does not specify any of this, as you noted. I can't find any mention of Hallow in the Sage Advice Compendium or the PHB Errata, and I couldn't find any unofficial tweets by Jeremy Crawford referencing this use of Hallow either, so we have little to go on as for the designer intent.

Recommended: Both

If the Frightened condition inflicted by the area is supposed to have any effect, then it doesn't really do us any good to only look at either the area or the point of origin - as you note, both lead to some absurd results that kind of defeat the point of using the option in the first place.

I'd recommend treating the "source" of the fear as the entire area for the purposes of determining if you can "see" it, and as the origin of the area for the purposes of moving closer to it. That might feel slightly inconsistent, but it leads to much more sensible results - you can move out of the area if you're in it, but not closer into it. You're also continuously affected by the disadvantage imposed by the frightened condition as long as you're in the area.

I can't prove that this is the design intent; it is merely how I'd expect an effect like this to work.