"He is going past our house to the restaurant."
Translation:Li iras preter nia domo al la restoracio.
Yes, if you want to emphasise that he did not stop there and continued further. Here is a helpful link that I saw in another thread discussing this question: http://bertilow.com/pmeg/gramatiko/rolmontriloj/rolvortetoj/lokaj_rolvortetoj/preter.html#i-arh
preter by, straight past, beyond, past
Li iras preter nia domo al la restoracio.
He is going past our house to the restaurant.
On his way to the restaurant, he goes past our house.
On his way to the restaurant, he is passing our house.
(Maybe our house is on the same road as the restaurant?)
post after, behind
Li iras post nia domo al la restoracio.
He is going after our house to the restaurant.
(Our house is going to the restaurant, and so is he, so he tags along ... ?)
(Our house seems to be able to move on its own ...
I think "n" is an ending which adds meaning of destination to prepositions which they initially don't have, so neither "al la restoracion" (because "al" is already a destination preposition) nor "preter domon" (because there is no destination "to somewhere past something" in the sentence) are good here.