New York Rangers in seven
Anaheim Ducks in six
San Jose Sharks in five
Ottawa Senators in five
(I decided that since I was going random, I would put pieces of paper numbered 4 through 7 and pick the number of games it would take for the win.)
My actual picks (sans number of games, because that is too complex for me):
I have a feeling that paper bag is going to fare a lot better than my personal picks.