It's pretty obvious where it takes place now to be honest.
It's a sequel to A Link to the Past; however, it is not a direct one - quoted to in fact take place "centuries" after the original events. So considering the Oracles and Link's Awakening are roughly direct sequels, that would mean A Link Between Worlds takes place after that set of games.
So like you said, this takes place some time after Link's Awakening, but I don't think it will link in with that game or show some form of continuity, as it's been heavily branded as an A Link to the Past sequel.