There is no proper darkness on the Curonian Spit in the third week of June. The sun sets late and lazily, the sky holds a pale blue for hours, and by the time you think night has arrived it is already turning back into morning. People stay out. Nobody is quite sure what time it is.
On the spit
The Parnidis dune above Nida is the place to be for it. The sand keeps the day's heat well past midnight, and from the top you can see the lagoon on one side and the open Baltic on the other, both of them lit by a sun that cannot decide whether to leave.
This is Midsummer, the biggest night of the year in Lithuania, Latvia and Estonia. There are bonfires on the beaches, wreaths on the water, and a general agreement to be outdoors for as long as the light holds, which is to say most of the night.
If you come in June
Build your trip around the third week of the month if you can, and do not over-schedule the evenings. The days are long enough that a late dinner and a walk after it still land in daylight, and the good hours here are the ones most itineraries waste indoors.
Bring a layer anyway. Warm light is not the same as warm air, and the coast cools down whether or not the sun agrees to set.