Pacific:  ANA, LA, SJ, PHX, VAN, CGY, EDM

Midwest:  DAL, COL, WIN, MIN, CHI, STL, NAS

South:  TB, FLA, CAR, WAS, DET, CBJ, PHI, PIT

East:  MTL, TOR, OTT, BUF, BOS, NYR, NYI, NJ

Note that there would be 16 teams in the Eastern Conference, and 14 in the West.  All teams based in the Eastern time zone would be in the East this way.  In fact, having 16 teams in the East slightly neutralizes that side's travel advantage, in that the East would have two more teams fighting for the same number of playoff spots.  As far as the West goes, you could draw a north-south line that would perfectly divide its two new divisions (see the league map here). 

If you wanted to make the argument that as many Canadian teams should share a division as possible, you could swap out Winnipeg and Phoenix (a highly ironic thing of me to say), but would the Jets be willing to trade off the vastly increased travel for the higher number of all-Canada matchups?  And I can't imagine Phoenix would be too thrilled about increased travel either.  Other than that, this makes the most sense to me. 

As far as the schedule, I'm not sure exactly how you'd break it down, but as long as every team visits every other team at least once a season, I'd be happy.  The NBA can do it; why can't the NHL?

(Of course, if all this happened and they got rid of the trapezoid, I'd be really happy.)