Just a super interesting graphic that the Storm Prediction Center put together using GIS data. What you’re seeing is a graphical representation of the track of each tornado that’s impacted the continental United States from 1950-2013. Notice the density in Tornado Alley, a region of the country where geography is conducive to the large scale weather patterns that produce tornadoes. Also, check out the general trend of a northeast vector to the tornado tracks. Lastly, note that although tornadoes are considerably less common in the Northeast, they still do occur with some frequency.
It is not impossible for a weaker tornado to form in this region, nor do the mountains somehow protect this region from tornadoes, they are just not as common of an even here as they are in the great plains and the deep south.
Absolutely right, tornadoes can form in any geography under the right atmospheric conditions. In fact, NYC has been hit by multiple tornadoes in the last 10 years. An EF2 hit Brooklyn in 2007, then in 2010, twin tornadoes hit Brooklyn and Queens in September, one right in my own neighborhood (https://en.wikipedia.org/wiki/2010_Brooklyn/Queens_tornadoes#cite_note-5), the photo on this article was taken by yours truly!