You are correct about (1) and (2)—CGEL would say they are locative complements in the form of a PP.
You are also correct about (3). CGEL does explicitly say that there is a preposition on p. 640, in the context of discussing prepositions whose complement is another PP:
The PPs here, there, now, then occur as complement to a wider range of prepositions than do such PPs as under the bed or after six. We find, for example, They live near here; Put it on there; I found it behind here; You should have told me before now; He certainly stayed past then.
However, CGEL says (p. 429) that today is not a preposition, but a deictic temporal pronoun:
Yesterday, today, tonight, and tomorrow are not traditionally analysed as pronouns, but belong in this subclass of nouns by virtue of their inability to take determiners. Compare, for example, Today/*The today is my birthday. They are also semantically like the central pronouns I and you in that they are characteristically used deictically. Unlike the temporal prepositions now and then, the pronouns have genitive forms: today's, etc.
As far as whether locative in locative complement is a syntactic or semantic characterization, CGEL seems to claim the former. On p. 257, in the section 'Relation between locative complements and predicative complements':
We will not assimilate the locatives to the predicatives, but will regard them as syntactically distinct kinds of complement that exhibit certain semantic resemblances.