Check your FDA climate zone.
Though you can grow palms in areas that you might not think can sustain them, there are limits. You need to live in zone 7 or warmer. The lowest temperature on the extreme end of the scale in zone 7 is 0 degree farenhiet. This is the limit for hardy palms.
Zone 7 stretches from Cape Cod, across the upper south and then along the western side of the Cascades and Coastal Range on the west coast all the way to the panhandle of Alaska. Yes you can grow palms in Alaska.
Pick a palm.
There are three types of palms that are likely to do well in more northern latitudes.
The Needle Palm
Generally considered the hardiest of all palms, it grows in small clumps 2 to 3 feet maximum. You might even be able to push this species into zone 6. I understand that there is a shrub growing in King of Prussia Pennsylvania.
Like the needle palm, the saw palmetto only grows to 2 or three feet. But in my opinion it is a more elegant plant.
It is native to Florida to as far north as Cape Hatteras North Carolina, but can be grown much farther north. This is a great plant to wow your neighbors with.
The “Windmill” or “Chusan” Palm
Native to the foothills of the mountains of south eastern China this beautiful plant is the only palm that will grow into a tree in zone 7. It can tolerate very hard frosts and snow with little difficulty. At the absolute northern frontier of plantability shield from wind.
The windmill palm is my personal favorite and can add an elegant tropical flavor to many gardens that now lack that flavor.