Well, "free health care" isn't exactly free. Read up on it. Living here as a Canadian, an immigrant, no matter who, you have to pay for government health coverage, which entitles you to your "free health care" at the point of use. Even then, there are restrictions.
What about "here" is making you want to move away? Have you travelled to anywhere in Canada before? If you're ok with climates you'd get in New York, just moving a bit north to southern Ontario or southern Quebec will be similar. Mountains out there aren't mountains if you ask me. The west coast has better mountains, and then the interior of BC, and the area closer to the BC and Alberta border has the Rockies, which are something else entirely, amazing places, but more extreme in the winter.
Based on the little info you've given, and what I'm interpreting as a lack of research and real reason, you need to read up on it. Moving to another country isn't as easy as I think you might perceive it as being, unless you are moving for school. Moving for school is the easiest way, but you are very restricted with how much you can work (less than 20 hours a week legally if I remember correctly). There are tons of resources on the web that can help. I had looked into moving to California before for visual effects, and the list of things you need to do can be overwhelming, and stressful too, as the entire process can hinge on one single decision that is out of your hands (finding work).