Long-time lurker, first-time poster. :)
My short list:
--Video: Strictly optional. I don't have the same enthusiasm for video on a photo camera that a lot of you seem to have, HD or no HD.
--Appearance: I'd like something that doesn't scream, "Look at my expensive camera!" Something that, unlike a DSLR, doesn't draw attention to itself or to me; in short, a camera that's good for street shooting pretty much anywhere, without being thief bait.
--EVF? Nope. I'd prefer a rangefinder, actually. Assume that the rear LCD would function both as control screen and for Live View shooting for those of us who occasionally find that sort of thing useful. Said screen would, hopefully, be an articulating screen of good resolution.
--Format: 4/3, though I have the sneaking suspicion that Nikon, like Canon (and Leica) will turn their backs on the format.
--Finally, as for the aesthetics of the thing: Something suitably retro, with plenty of manual controls. As Olympus has done with the PEN line, Nikon could look back to its own past (say, the Model S Nikkor rangefinder camera) for design inspiration.