With the assumption being that Phoenix moves to Winnipeg, this is onw way I'd redo it. Eliminate the conferences. No Eastern and Western Conferences, cuz let's face it.....half the teams in the west are really east/central. I'd put all the teams into 3 team divisions.
Divisions:
Vancouver, Calgary, Edmonton
San Jose, Los Angeles, Anaheim
Winnipeg, Minnesota, Chicago
Colorado, Dallas, St. Louis
Ottawa, Montreal, Boston
New Jersey, New York (R), New York (I)
Detroit, Toronto, Buffalo
Pittsburgh, Philadelphia, Washington
Columbus, Nashvill, Carolina
Atlanta, Tampa Bay, Florida
Games split up into:
16 games against each team in your division (8 games per team)
42 games against 7 other divisions (2 games per team nets you a home and home against every team in the NHL)
24 games against 2 other division (4 games per team)
82 games total
Playoffs:
Division winners make the playoffs guaranteed, while there are 6 "wild card" teams which make it based on points. Rankings of these 16 teams are done strcitly by points, so you could have a dvision winner in #16. Teams pair off #1-16, #2-15, etc. or the Swedish Elite League system could be adopted, where the top 4 teams select their first round opponent. For example, #1 could select #11 because their starting goalie got injured in the last week of the season. #2 could pick #5, because they beat them 8 times during the season. Whatever 8 teams remain, they would be ranked by points, and the highest and lowest pair off.
Cross country road trips would be early in the year, and they would be big ones (7-8 games) since players are fresher at the beginning and wouldn't be as fatigued by the road trip. Also, before and after this trip the team would have 2 days to rest. I'd totally eliminate back to back games. There's enough days in the season where teams don't have to play back to back games, and it reduces the risk of players getting injured.
With respect to rivals, most of these divisions have at least one close rivalry, and a rivalry gets reborn (Toronto-Detroit). There are 2 divisons without any rivalries (Winnipeg, Minnesota, Chicago and Colorado, St. Louis, Dallas) but with 8 games against each team, rivalries should develop quickly. And, anyhow, they still play at least 2 games against their other rivals. Also, to increase the formation of the rivalries, I'd put the majority of games (4-5) against each team in your own division within the last 3 weeks. If your team doesn't make the playoffs, you're really going to be pissed off at the other teams.
With the 24 games against 2 other divisions, you could make it so that teams play against the same division every year, or you could change them around (I'm in favour of changing them around).
