Is 'place' functioning as an adverb or is the relative 'where' dropped in these sentences?

1)Of course it’s always the last place you look. (no ‘at’)

2)This is the last place I want to go. (without ‘to’)

compare 3) with 2)

3. This is the restaurant that we often go to on the weekends.
   There is ‘to’ after ‘go’.

So can ‘place’function as an adverb especially when it’s modified by some clauses? And regular nouns of place like ‘restaurant’ can’t? Or is it that the relative ‘where’ often gets dropped after ‘place’? It’s sort of like a zero-relative-conjunctions situation here? like the day I graduated?