Good Places for Hiking and Nature Near Copenhagen?

Hi all,

The weather forecast is beautiful and warm! But where to go? After being in city life, we are craving a nice day trip in nature.

Where are some good destinations for a hiking day trip from Copenhagen?

The more details the better!! -I have found some places online, but I am having trouble to get the the travel details (address, ect) for how to reach there - and then trail maps,ect for hike planing.

Please share your experiences and suggestions :)

Thanks!