Green Castle Woods
This is found between Johnstown and Llansteffan (on Llansteffan road). It's a really gorgeous place for a walk and picnic, the woods have been untouched for hundreds of years and apparently was frequented by Henry VIII and his motley crew. Between April-early June it's carpeted with bluebells and it's FREE!!!
(I would not advise this for anyone with mobility difficulties, there are a lot of hills, steps and tree roots!)