Where nostalgia expresses a longing to return to time or place when things were good, it is tinged with melancholy, even sadness and anxiety. Natsukashii, on the other hand, is absent this gloominess and suggests something slightly different: a happiness to be remembering a happy memory.
I listened to the word dozens of times during a single broadcast, sometimes succumbing to giggles. Such is the mental exhaustion caused by straining to learn a language with no classes and little written material. Or, the emotional exhaustion of trying to faq out a life as an alien in a new land.