Yes, each of the big 4 North American professional sports leagues will expand to smaller markets if they get more money, but when it comes to which type of team they want in the finals, they would usually prefer to have a bigger market team to boost television ratings.
The NHL is coming off an amazing year in which it saw the success of the Winter Classic, Heritage Classic, Stadium Series, an exciting playoffs, television deals, and tons of revenue. A Stanley Cup Finals between the two largest television markets in North America, New York and Los Angeles, is an amazing way to top it off.
The NHL has wanted a Stanley Cup Finals like this fo a long time. It is a classic East vs. West, L.A. vs. Big Apple, Hollywood vs. Broadway finals. More importantly for the league, however, is the potential for huge T.V. ratings. Yes, the Los Angeles Kings beat the New Jersey Devils in 2012, but the New York Rangers are a franchise with an amazing history and a top-5 NHL fanbase, unlike the Devils. If the Rangers and Devils were both playing on the same day against different teams, more New Yorkers would watch the Rangers simply because they are more popular. That is why the team participated in two Stadium Series games. This goes for the Anaheim Ducks, who are a successful franchise, but are not as popular as the Kings; and the New York Islanders, who have been subject to many losing seasons in the past decade and are inferior to the Rangers when it comes to a fanbase.
Another reason why the NHL and other pro sports leagues like to have a big-market finals is because the league will be popularized in the markets. Although New York is an established hockey city, if more non-hockey fans from Los Angeles (which has more potential to grow as a hockey market) tune into NBC or one of their stations on the night of the game, they will be more interested in cheering for their home team. Since Los Angeles has such a high population, then more people will be doing that.
While the NHL may be capitalizing on a once-in-a-generation opportunity here, horse racing will be looking to capitalize on a similar situation with California Chrome (a fan of the Anaheim Ducks) to race for the Triple Crown in none other than New York in the Belmont Stakes.
Whoever wins the Stanley Cup, it is still a win-win situation for the league. So, they probably want it to go to as many games as possible.