It's tough to say right now, there's likely to be lots of moves at the draft and in free agency.
I know the Sedin's are just going to get older, but Vancouver's owner does not want them to tank, so they might make some more desperation Loui Eriksson type moves that could keep them out of the basement.
I think Detroit is a good pick, because with them missing the playoffs they might decide to bottom out for a year or two.
Colorado is the obvious choice, but there's likely to be a major shake-up there this off-season with any or all of Duchene, Landeskog, or Barrie being dealt. I'd want to wait to see how the dust settles before making any predictions about them.
My pick would be New Jersey, I just don't like the way that team is constructed, especially with Schneider's poor play this season. They remind me of the Leafs when we had Kessel, they have a star winger, and mediocre everything else, and that's not a recipe for success.
One wildcard pick: if JT is dealt, the Islanders could be in the mix.
EDIT: I forgot about Vegas, although I would exclude them from this discussion because their situation is so unique.