I remember discussing this very question in my “Fantasy Lit” class back in college. The professor pointed out that in classical romantic “quest” fiction, the hero successfully ends his quest with his society restored and he himself in his optimal relation to it, fitting in like a key in a lock. Classically, he is socially elevated and married. (I think G.K. Chesterton actually said that the natural end of the hero’s tale is a wedding.)
So by this standard - Tolkien was a literary scholar, after all - Sam is indeed the hero of LoTR. He earns the rewards of the virtuous knight errant triumphant, and finishes the novel a husband and a father, Mayor of Hobbiton and master of Bag End, fully integrated in the restored order of creation. He has the very last line of the story: “I’m back.”
Frodo, on the other hand, is the Tragic Hero, who never does find healing in the world. He has to leave it to find peace. And let’s not forget that Frodo, heroic as he is, failed his Quest.