What happened to the Marauder's Map during the 7th book when Harry and friends were out hunting Horcruxes?
Harry had it
He packs it shortly before the Wedding, when the Trio are preparing their getaway bags (emphasis mine):
Up in the attic room, Ron examined his Deluminator, and Harry filled Hagrid's mokeskin purse, not with gold, but with those items he most prized, apparently worthless though some of them were: the Marauder's Map, the shard of Sirius's enchanted mirror, and R.A.B.'s locket. He pulled the string tight and slipped the purse around his neck
Harry Potter and the Deathly Hallows, Chapter 7: "The Will of Albus Dumbledore"
And he uses it after Ron storms out of the tent, initially to watch for Ron, but eventually to
spy on gaze wistfully at Ginny's dot:
Meanwhile Harry had started bringing out the Marauder's map and examining it by wandlight. He was waiting for the moment when Ron's labeled dot would reappear in the corridors of Hogwarts, proving that he had returned to the comfortable castle, protected by his status of pureblood. However, Ron did not appear on the map and after a while Harry found himself taking it out simply to stare at Ginny's name in the girl's dormitory, wondering whether the intensity with which he gazed at it might break into her sleep, that she would somehow know he was thinking about her, hoping that she was all right.
Harry Potter and the Deathly Hallows, Chapter 16: "Godric's Hollow"