Truly grateful for the generosity of care, thought, and effort in these responses - thank you all so much.
Since the initial post, we have become so enamored with so many places that we've extended our post-Stockholm trip to two weeks. It stretches the budget a little tighter - we just started our respective post-grad student piggy banks - but we figure, two weeks of immersion beats one week of (relative) splendor.
The current idea is three days in London, a trip on the chunnel followed by three days in Paris, and then eleven days on the wind, day trips and then staying longer when we feel a a particularly profound pull. Thanks to the responses here, the current destinations are: Barcelona, Madrid, Bruges, Rome, Vienna. (There's one to-be-decided spot there, too. Habibi - Budapest would have made it if Samantha hadn't been there twice already.)
We both love the idea of travel as a negation of cultural assumptions - being reminded that many truths, imperatives, luxuries that add up to personal happiness are distinctly American and that there are other, often better, alternatives. (This is culinarily true, as well.) We're hoping that going to more cities will be like beating the windshield wipers a few more times across the glass.
Plus, we walk like New Yorkers. (New Yorkers predisposed to awe, anyway. We passed the Hancock walking home last night, and it was enshrouded in fog and looked like it extended into the sky, like some gothic Tower of Babel. We stared up for so long that I had to fend off other Chicagoans volunteering directions.)
So, I think our trip now becomes a combing and culling for must-visits and highlights, neighborhoods and hostels. I've looked through older posts and found a number of excellent suggestions, but new thoughts are always welcome. Or any other insight for two people about to dive into Europe, really. I would love a pair of floaties.