You probably mean 'days of yore'.
Yore means time long past and is a corruption of the middle english word for long ago, or year.
Halcyon is from the Latin/Greek for the kingfisher bird. A fabled bird, that was supposed to have had the power to calm the wind and the waves while it nested on the sea during the winter solstice. Hence, halcyon days are akin to a golden era when all was peacful and calm and tranquil.
More often both refer to simpler (childhood) times when worries were less.