at a lower place vs to a lower place

at a lower place and to a lower place both are adverbs.

Word	Noun	Adjective	Verb	Adverb
at a lower place	No	No	No	Yes
to a lower place	No	No	No	Yes

As adverbs, at a lower place and to a lower place are synonyms defined as:

Other synonyms of at a lower place include below, beneath.

at a lower place (adverb)	to a lower place (adverb)
in or to a place that is lower	in or to a place that is lower