local post office vs post office

local post office and post office both are nouns.

Word	Noun	Adjective	Verb	Adverb
local post office	Yes	No	No	No
post office	Yes	No	No	No

As nouns, local post office and post office are synonyms defined as:

local post office and post office: a local branch where postal services are available

local post office (noun)	post office (noun)
a local branch where postal services are available	a children's game in which kisses are exchanged for pretended letters
	a local branch where postal services are available