Where does he come from?
He didn't let on where he was off to.
Where to live.
be where it's at
Even though "where" is used as an adverb or conjunction mostly, it doesn't seem so in the case above but rather a noun as followed by infinitive or refered to preposition. But none of dictionaries says that it can be used as a noun.
What part of speech is 'where' meaning in such cases? Do they still act like adverb?
The part of speech of the word where is somewhat ambiguous. It all depends on how you look at it, because it isn't uncommon for the word itself functions as different parts of speech at the same time.
Adverbs, by definition, is a word that modifies a verb, adjective, a fellow adverb, or a group of words. In your examples, the word where still acts as a modifier.
Where does he come from?
While Where answers the question of location, qualifying it as an adverb, it also qualifies as a pronoun, as it is capable of acting as the subject, replacing a noun phrase like "What place".
He didn't let on where he was off to.
In this case, you can also consider where to be both adverb and conjunction. Modifying the phrase off to as an adverb, and connecting the two clauses.
...where to live.
where in this phrase, acts as an adverb, modifying the verb live.
The entire phrase where to live can also act as an adverbial phrase given the appropriate subject. For example:
They are having trouble deciding where to live
Where the phrase modifies the verb deciding.
...be where it's at
While I couldn't think of a complete sentence off the top of my head for this case, the entire phrase where it's at functions as an adverbial phrase, denoting location for whatever the subject could be.
