I was here in April. Wonderful stay, despite I checked in before 22:00 on a weekday and the Restaurant was already closed. You come to Skovshoved Hotel if you fancy atmosphere, old charm, specific danish old and new design. To be considered is the possibility of seaside walks -this coast is a jewl on its own. You may visit Copenhagen from here, and also discover the other sites of Sjaelland (Helsinghor, Hillerod, Klampemborg and the countryside).
It's positioned as premium hotel and I believe it fits expectations -but remember: it's an old, charming Danish house, not a modern, refurbished international hotel.