For three weeks each summer the sleepy town of Gråsten (population 4200) is abuzz as Queen Margrethe and Prince Henrik (and usually the extended family) head for some R&R at their summer residence, Gråsten Slot. When they’re not visiting, the lovely palace garden is open to the public; it makes a good excursion from Sønderborg. The garden's seasonal closing times vary, from 4.30pm in winter to 8pm in summer.
Gråsten Palace is on the banks of the lake, Slotssø. It was originally built in the middle of the 16th century but destroyed by fire in 1603. It was rebuilt, only to be ravaged by fire again in 1757; in 1842 the main building you see today was constructed, and in 1935 the rights to the castle were handed to the royal family.
The only part of the palace open to the public is the richly adorned chapel, built between 1699 and 1702 and the only section of the old castle to survive the fire of 1757.
Trains between Kolding and Sønderborg stop at Gråsten (from Sønderborg 42kr, 12 minutes). Buses 110 and 223 cover the 16km between Gråsten and Sønderborg (42kr).
The best way to check if the royals are at Gråsten is to ask around (including at local tourist offices), or check online for royal family activity (http://kongehuset.dk/en). In summer, signs are posted on the garden gates indicating dates the site is closed to the public.