What is the preposition in this sentence after the movie, we will grab a pizza to take home?

The correct answer is after.
Prepositions usually point to a location (in, on, under), but can sometimes refer to time as well, as in the sentence above. The word after can be used either as a preposition (which is the case here), or as an adverb. The difference is that prepositions are used with nouns, whereas adverbs are used with verbs or clauses.