We inherited the cottage, so have had many happy years of experience of the area. It is less than an hour's drive from Copenhagen airport, and 2 hours from Roedby, with the car ferry to Puttgarden in Germany.
Sletten is an old fishing village with a sailing harbour (and a good fishmonger, supplied partly by local fishermen), full of thatched cottages. There is a local sandy beach perfect for families, with a bathing bridge in the summer and shallow, calm water stretching out at least 100m into the sea.
Within 20 mins' drive or train ride are Elsinore (Kronborg, good shopping and restaurants), Fredensborg and Rungsted / Horsholm, with good local museums including Karen Blixen's house. The internationally renowned Louisiana gallery is a 20 min walk, and Copenhagen is 1/2 hour's drive.