From the SOED can be got the following definitions.
show 11 b Guide (or lead) a person, to, into, over, or through, a place, house, etc. [since] Late Middle English.
show round show (a person) over a place, show the sights to.
"To the house" is correct according to the Oxford dictionary. However,the phrasal verb "show sb around/round (sth) is used more commonly; it can be taken as synonym when used with "through".
show around phrasal verb
show somebody around (something)
(British English also show somebody round (something))
to be a guide for somebody when they visit a place for the first time to show them >what is interesting
♦ We were shown around the school by one of the students.
These ngrams shows that the form using "around" is more common: (ngram 1, ngram 2). I suspect that "show sb to (a place)" is more formal.