There's more than a particular place involved.
The verb set is the (transitive) causative form of the verb sit.
I.e, set X means 'cause X to be in a sitting position in some location':

• The statue used to sit on the mantelpiece. ~ He set the statue on the table.
• Bill sat down in the corner ~ Bill set himself down in the corner.

A similar situation obtains for the verb pairs lie ~ lay and rise ~ raise.
All of these refer to characteristic human bodily motions,
metaphorically extended to other phenomena.

The difference between (say) setting it there, laying it there, and standing it there
depends more on the shape and disposition of what it is than anything else;
all of them mean 'put' or 'place'.

There's more than a particular place involved.
The verb set is the (transitive) causative form of the verb sit.
I.e, set X means 'cause X to be in a sitting position in some location':

• The statue used to sit on the mantelpiece. ~ He set the statue on the table.
• Bill sat down in the corner ~ Bill set himself down in the corner.

A similar situation obtains for the verb pairs lie ~ lay and rise ~ raise.
All of these refer to characteristic human bodily motions,
metaphorically extended to other phenomena.

The difference between (say) setting it there, laying it there, and standing it there
depends more on the shape and disposition of what it is than anything else;
all of them mean 'put' or 'place'.