This is the theory I've heard the most:
4 divisions...
East South
Boston Bruins Florida Panthers
Toronto Maple Leafs Tampa Bay Lightning
New York Rangers Carolina Hurricanes
New Jersey Devils Nashville Predators
Philadelphia Flyers Washington Capitals
New York Islanders Pittsburgh Penguins
Montreal Canadiens Detroit Red Wings
Buffalo Sabres
Pacific Midwest
San Jose Sharks Colorado Avalanche
L.A. Kings St. Louis Blues
Phoenix Coyotes Minnesota Wild
Anaheim Ducks Ottawa Senators
Calgary Flames Dallas Stars
Edmonton Oilers Columbus Blue Jackets
Winnipeg Jets Chicago Blackhawks
Vancouver Canucks
The first round of the playoffs would be divisional match-ups, 1 vs. 4, 2 vs. 3. The teams would then be re-seeded by conference and again, 1 would play 4 and 2 vs. 3. While I don't necessarily agree with the above positioning of every team (I would be sad to have Chicago and Detroit in separate divisons for example), I think having the first round be divisional match-ups again is an absolutely fantastic idea that will spawn many new rivalries and even re-kindle some old ones.