I am interested in visiting the Curonian Spit, possibly with a sidetrip to Kaliningrad. Now I would like to know the best time of the year to do so. I would like to avoid the crowds of the high and peak seasons. On the other hand, I would like to avoid the dead season (if there is one) as well, when most of the restaurants, shops and attraction are likely to be closed. Also note that I do not care about temperature.
Sorry for the late answer.
First of all, I want to mention that my mother is from Kaliningrad, and I've spent nearly half my life there, especially during summer holidays. And now about your question.
Dead season is from November to March. During this period you should visit Kaliningrad only if you have direct contact with some locals who can help you with transfer (quality of the roads outside the town is very low). In 2007 a skiing base was opened in Ozersk, but it is hard even for locals to get there, so this is an extreme option :)
Need to note that sea and Curonian split are very beautiful in this period, especially if there's some snow.
Some activity starts in April and May - snow is gone, but crowds are not there yet, only children for small school holidays, but weather is not very good.
Second half of May and June is a fine variant for you in general - the sea is not so warm and not many people will come - only adults with children for summer holidays.
As already mentioned, July and especially August are very crowded months, and I don't recommend visiting during this period, if you don't have direct contact with locals. Also need to mention - the weather becomes rainy in the second part of August.
My favorite season is September - the sea is still warm, but children are in school already, and tourists are already back at their jobs. Beautiful places and good weather - that's all you need to find in Kaliningrad.
Also need to mention that October is an option too, but some reastaurants and shops are already closed.
I forgot to say that in June, 2012 the European cup will take place, and many fans of the Russian team will be based in Kaliningrad - near Poland, where the games will take place, and you'll have extreme trouble getting some place to rest, so try to avoid a trip in this period.
I was never really in this region, but last summer when I went to Estonia, Russia and Latvia I thought about going to Kaliningrad and the Curonian Spit as well. For that I read a lot about the best time to go there.
Over the winter it can get a little bit cold, but you don't care about that- Nevertheless most attractions and other things tend to be closed over the winter. In the early spring season (March, maybe even April) you will have a lot of rainy day. The Lonely Planet Eastern Europe guide says:
Avoid March and early April - the "thaw" is the least pleasant time since the grey weather and general muddiness make walking about unpleasant.
In the high season during the summer (July, August) it can get very hot and a lot of tourists are in the region. It can get a little bit crowded. So I would prefer to go either on May/June or September/early October.
The Lonely Planet says the same:
The best months to visit are May, June and September.
For the Lithuanian side the high season is July and August, but really it is weather dependent. Expect much more people when the sun is shining in the weekend, since Curonian Spit is easily accessible from the mainland, and the access is from a large city (3rd largest city in Lithuania, large of course in relative terms, population 200k) Klaipėda. So when weather is good there is an influx of local population. Even in the high season crowds are manageable, since the prices are relatively high.
There are 4 villages in Curonian Spit, Juodkrantė, Pervalka, Preila and Nida. All the crowds are usually gathered in Nida, so you can try other 3 villages, of which I recommend Juodkrantė.
There is a cycling trail from Klaipėda to Nida (about 40km), which goes along the sea, it is never crowded.
The dead season is when bad weather starts in October and ends in April. There is a bit of activity in holiday season, but that's it. But since the main attraction of Curonian Spit is its nature, not restaurants, you can stay in Klaipėda for the attractions, and visit Curonian Spit for the sights.
Cannot give any advice for the Russian side, since I never been there. There is a bus from Klaipėda to Kaliningrad.