Is there a term that defines nostalgia for something you've never experienced?
Solution 1:
I think the word wistful captures that sense of wishing for something, tinged with regret. I'm not sure that nostalgia requires you to have experienced the thing you're missing, but it does require it to be in the past. Wistfulness doesn't - I can feel wistful thinking of something I could be doing, or had once thought I would be doing by now, and neither of those fits nostalgia.
Solution 2:
There is a term advocated by C.S. Lewis and others that fits the bill: sehnsucht.
http://en.m.wikipedia.org/wiki/Sehnsucht
I've been known to use this term for its direct meaning as a "longing and nostalgia for a far-off home one has never visited," but it can be inflected or further defined to describe what you mean. So far, it's the most satisfactory English (technically, German) noun I've found to describe this phenomena.
Solution 3:
I think "yearning" captures a fair portion of that feeling.
References:
"A persistent, often wistful or melancholy desire; a longing."
"a strong feeling of wishing for something, especially something that you cannot have or get easily"