The Vancouver Canucks are the closest NHL team to Seattle. In regards to flying distance, the Calgary Flames are the next closest, followed by the Edmonton Oilers, the San Jose Sharks, and then the Colorado Avalanche in Denver. With the exception of Calgary and Edmonton, that probably makes sense to most sports fans.
Canada has seven NHL teams: Vancouver, Calgary, and Edmonton, of course, but also the Winnipeg Jets, the Toronto Maple Leafs, the Ottawa Senators, and the Montreal Canadiens. For an American sports fan who's not necessarily into the NHL, while we're all aware of Canada being north of the United States, it may take some getting used to the fact that there's more than one Canadian-based team in the league. And if you're an NFL fan that's only very casually interested in hockey, then mentally including Canada into your sphere of serious athletic interests may require a bit of doing.
The Vancouver Canucks are a part of the NHL's Northwest Division in the Western Conference. The teams within this division are Vancouver, Edmonton, Calgary, Colorado, and the Minnesota Wild.
The California teams are in the Pacific Division, which includes San Jose, the Los Angeles Kings, the Anaheim Ducks, the Phoenix Coyotes, and the Dallas Stars. The likely reason behind doing a northern & southern division scheme is to keep the Canadian teams together. That's personal speculation, but it's totally something that the NHL would do.
You'll see this a lot in the NHL. There's a great deal of Canadian teams versus everyone else. Canada believes that they're the originators of hockey, so Canadian-based teams have a lot of say in what goes on in the NHL. Even if at times they feel as if they don't.
Incidentally, the NHL's Canadian offices are in Toronto. In the Air Canada Centre, in fact, which is where the Maple Leafs play. Their "War Room" - the centralized instant replay location for all of the NHL, where they review and make the final call on questionable hits, penalties, or goals - is also in the Air Canada Centre. The NHL's American offices are in New York City and were at Madison Square Garden, home of the New York Rangers, but have since moved uptown a few blocks to between 46th and 47th Streets on 6th Avenue.
The last division in the Western Conference is the Central Division, which includes the Chicago Blackhawks, the Columbus Blue Jackets (Ohio), the Detroit Red Wings, the Nashville Predators, and the St. Louis Blues.
If you've been keeping track, you may wonder what happened to Winnipeg - why aren't they in the Western Conference? As of right now, the Jets are still a part of the Southeast Division in the Eastern Conference. The Atlanta Thrashers had moved so abruptly that they didn't have time for the process of realignment, so they left them in the same division and conference even after the move. They play in the same division as the Washington Capitals, the Carolina Hurricanes (who are in Raleigh, North Carolina), the Tampa Bay Lightning, and the Florida Panthers.
League realignment will happen, but it will be a part of the new collective bargaining agreement (CBA) that's currently being hammered out by the NHL and the NHL Players' Association (NHLPA). When the NHL came up with a new configuration last year, they'd left what looked to be two slots for expansion teams - one new team in each conference.
The NHLPA wouldn't ratify the league's idea as they were not a part of the development process, so it's now a part of the CBA talks. Therefore, the league's conferences and divisions will stay this coming season as they were last season. Any agreed upon changes will go into effect in 2013-2014, despite the new CBA going into effect on (hopefully) 16 September of this year.
Which is probably just as well since the situation with the Phoenix Coyotes is still unresolved. It has been speculated that if they moved, it would be to Quebec City, as they've got people ready to buy the team and will be breaking ground on a new arena next month. As it stands now, the Coyotes will almost certainly stay in Arizona for at least one more season, since even if they were sold to a group in Quebec City, it's too late to move them for the coming season.
If/when Seattle gets an NHL team, they will probably play in the same division as the Canucks. As well as with Calgary and Edmonton. After that, it's hard to say who else would be a part of that division. If the realignment scenario that the NHL presented last season stays relatively the same, then there's a possibility that the NHL team in Seattle could be an expansion team instead of a relocated NHL team.
We'll just have to be patient until the NHL and the NHLPA agree to a realignment scheme to get a better idea of that.