You're correct when you say that 'here' is not the subject, In your sentence, 'here' is an adverbial complement. That means it is an adverb that completes the predicate and not, as you correctly point out, the subject. The subject of your sentence is 'task'. That may not seem obvious because it follows the verb rather than preceding it which is what we would expect in the commonly seen subject-verb-object sentence, but you should be able to see it if you just re-arrange your sentence like this: 'Your task for tomorrow is here'. I think that with that word order, the subject is clearly 'task'. By the way, I'm not suggesting you should use the re-arranged word order. Your original sentence sounds natural and it's what native speakers would say if they were handing out tasks, I'm just showing the re-arranged word order to make it clear why the subject is 'task'. Hope this helps.

task