I suppose that really depends on what you mean by 'heroes'. Several characters are backed into corners, and act in ways they might not prefer to. Other characters behave in a manner matching the 'realpolitik' of the world, which is filled with shades of moral ambiguity.
There are, however, many characters who are both good and heroes. Bran, Jon Snow, Ser Davos, Ned Stark, and Rickon are all heroes. Daenrys could be considered heroic, even if her methods are not always so..and certainly many of the knights, such as the runaway knight in disguise with Dany, are virtous in their own right. Both sisters and Rob Stark are good people, even if they either turn a blind eye to some things, or (in Arya's case) commit violence. Arya is, IMHO, one of the most heroic, in that she's fighting against so many injustices one could lose count. Her travelling companions are certainly good people, as was her fencing teacher. The same applies for the Maesters, to some degree.
If you're looking for a hero with no flaws who makes no concessions to evil, self-interest or mediocrity, then you've come to wrong place.
