On TV isn't so bad, but you would have to have seen some games live to have the same perspective.
It's an interesting comparison, actually. When I watch games in person, I actually feel more in the moment, but less tense. I'm just happy to be there, a sort of weird, soothing focus that feels great. It feels better in person, regardless of the outcome. (Although I do get passionate - if I'm not working, I'm free to scream.)
When I'm watching a game at home, I feel a great deal more tension, particularly when the stakes are high. Maybe part of it's the environment? With broadcasts, you've got your anchors, commentators, and color going on about how Player X hasn't produced numbers like he should, how Player Y is still injured, etc., whereas at the actual game you're surrounded by thousands of happy fans and an announcer saying, "Remember, check your ticket stubs for the chance to win a..."
The perspectives shift, too. Via broadcast, the ice surface always looks huge to me, yet simultaneously like the players have little room to move. In person, it's the opposite - the rink's just as modest as I remember it, and yet, there's a lot of open space to navigate. Maybe that's just me, though.
I think seeing games (of any league) in person is what it takes to hook someone, and then once addicted, it's like cocaine. At this stage, TV will suffice. You'll be happy to get anything, really. Downloadin' apps and whatnot to be updated on every goal.
[MENTION=4939]kyuuei[/MENTION] - If you don't live in/near a city with an NHL team, are there any other leagues accessible to you? AHL, USHL, NAHL? Any college teams? Although I've seen high prices at certain universities (D-I), tickets are typically much more manageable when going this route. Junior league games are very affordable if you wanna check out one of those, and they're still a great way to have fun and enjoy the sport.