Who said anything about him going to New York to do the Mixtape? Yes, we know that they end up in New York but I very much doubt that trip will have anything to do with the Mixtape.
The thing is with OUAT we cant say we know things with 100% sure, the mixtape may or not may be related to NY, but since the episode name has a sort of connection to Neal, since is a song that Henry only knew bc of his father, neal`s apartment may appear again( really hope not, no more bait/fanservice neal related, that should ahev been done on S3b and s4a) and with Henry in NY, i say there is a chance the mixtape being related to NY trip. But we will have to wait and see if is or not related to Ny trip.