Under the table is the place to look.

Yes: the PP "under the table" is the subject here.

This can be demonstrated by the possibility of having an interrogative tag, "isn't it?", where "it" is anaphoric to "under the table" , showing that the latter is subject.

The basic interrogative test for subjects also proves it's the subject: "Is under the table the place to look?"

Under the table is the place to look.

Yes: the PP "under the table" is the subject here.

This can be demonstrated by the possibility of having an interrogative tag, "isn't it?", where "it" is anaphoric to "under the table" , showing that the latter is subject.

The basic interrogative test for subjects also proves it's the subject: "Is under the table the place to look?"

Edit, as requested in comments:

There is no subject-dependent inversion here, as there would be in, say, On her desk was a bowl of fruit, where the PP on her desk is not the subject but a preposed locative complement.

Under the table is the place to look.

Yes: the PP "under the table" is the subject here.

This can be demonstrated by the possibility of having an interrogative tag, "isn't it?", where "it" is anaphoric to "under the table" , showing that the latter is subject.

The basic interrogative test for subjects also proves it's the subject: "Is under the table the table to look?"

Under the table is the place to look.

Yes: the PP "under the table" is the subject here.

This can be demonstrated by the possibility of having an interrogative tag, "isn't it?", where "it" is anaphoric to "under the table" , showing that the latter is subject.

The basic interrogative test for subjects also proves it's the subject: "Is under the table the place to look?"