How does doing the right thing not, necessarily, lead to happiness in the play?By the end of the play, Antigone's views on "doing the right thing"...

thanks pmiranda--yes, Creon is wrong for most of the play--he's the tragic hero, whose in his hubris, his overweening pride, encroaches on the gods realm-- he elevates himself above their law.  Similarly, Oedipus encroaches with "Your birds-- / what good were they?  or the gods, for the matter that? / But I came by, / Oedipus, the simple man, who knows nothing-- / I thought it out for myself, no birds helped me," and the play single action dramatizes his being put back in his place--the gods show his his moral limits--and Oedipus feels great misery and he suffers but now that he recognizes his identity, he knows himself and only in that knowledge can he be happy.  

In Antigone, Creon encroaches with "the gods? / Intolerable!  The gods favor this corpse? Why?  How had he served them? / Tried to loot their temples . . . / Is it your senile opinion that the gods love to honor bad men? / A pious thought!"  Creon raises his proclamation, his view of the law above the gods' law, and for the rest of he play, the dramatic action brings him in line with the fundamental law of the gods--"Nothing too much."  The artistic expression of the tragic hero's fall is an absolute good that celebrates a universal order--Necessity always rights man's place beneath the gods. 

So when the play brings Creon in line--when he tragic falls in line--with the moral order of the universe, Creon feels bad, of course, but happiness is that he knows his limits.