Rangers - They will start the season strong and finish first with a tough defensive system and good goaltending , although gradually tail off late in the season and have a short playoff run.
Penguins - I would normally pick the Pens to finish first but with the upheaval in the coaching positions combined with Maatta and Poiliot missing half the season I think they will struggle a lot at first. However, I expect them to finish strong and make a deep playoff run.
Blue Jackets - Their size and physicality paid off last season and will continue to pay off this season. With more talent they would be much like many of the better Western Conference teams like LA.
Islanders - I think they will establish some consistency and have a decent showing this year, although their place as fourth on this list is mainly because I think the teams beneath them will do so bad.
Devils - Still recovering from the damage from the Kovalchuk years (the players lost). However, this team traditionally has relied on mostly average players playing a tough defensive system and they are probably only a few years away from being able to reestablish that. Sure, Brodeur may be the best goalie in NHL history but any NHL goalie could play behind some of their defenses of the late 90's/early 2000's. Once they reestablish that Schneider should have no problem.
Hurricanes - meh
Flyers - On paper this team shouldn't have made the playoffs the last few years. The loss of Hartnell combined with the likelihood of Mason cracking at some point (and having to rely on Emery) will result in them finishing in a more appropriate spot.
Capitals -
It should be interesting to see how Ovi reacts when Niskanen shoots every time he touches the puck (instead of passing to Ovi). Trotz may be a good coach but I don't think he will be able to do anything with this team. In fact, I expect them to finish last in the league.