West

VAN v. LA
Vancouver won 2 games in regulation, Los Angeles won 1 in regulation and 1 in OT/SO. Vancouver is just on a roll, 8-1-1 in their last 10. They don't stop here.
I pick VAN in 5.

STL v. SJ
St. Louis won ALL 4 games in regulation against San Jose. I don't think they sweep the way they played at the end of the year.
I pick STL in 5.

PHO v. CHI
Phoenix won 2 in regulation and one in OT/SO, while Chicago won 1 game in regulation. Both teams are hot coming into the playoffs, but Toews
I pick PHO in 7.

NASH v. DET
Detroit and Nashville split 6 games all won in regulation (3-3). Nashville has home ice, so...
I pick NASH in 7.

East

NYR v. OTT
Ottawa won 2 games in regulation and another in OT/SO, while the New York Rangers only won 1 game v. Ottawa. It seems like the East always produces one big upset.
I pick NYR in 7.

BOS v. WASH
Washington won 2 games in regulation and another in OT/SO, while Boston only won 1 game v. WASH.
I pick WASH in 6.

FLA v. NJ
Florida won 2 games in regulation while New Jersey won 1 game in regulation and one in OT/SO. Florida backed their way into the playoffs with the worst final 10 games out of all of the playoff teams - and the fourth worst record in the NHL over that time period.
I pick NJ in 6.

PIT v. PHI
Philadelphia won 3 games in regulation and one in OT/SO, while Pittsburgh only won 2 games against the Flyers this year, both in regulation. Pittsburgh is finally getting healthy, so...
I pick PIT in 6.

That would set up the second round as VAN/NASH, STL/PHO, NYR/WASH, and NJ/PIT.