TL;DR - Want to leave NYC for a place with better COL, nature and has more cold days than hot

COL on NYC is ridiculous. I'd like to own a house at some point in my life. Before I do I plan to rent and save up for a down payment. Studio apartments that aren't in the worst areas are 1,700-2,000 here. I also have grown tired of being packed in with so many people and the awful air quality and general hygiene of the city. So I've been looking up states and taking suggestions of where I should visit to build my future in.

I'm 25 years old, full time accounting student living at home with my parents and working accounts payable part time. My significant other, 24, who will be moving with me is in a similar situation except is studying online to become an elementary school teacher.

My current plan is to finish up my bachelor's and then find a state to rent in. Currently, I end up with a surplus of around 30% of my take home that is all being saved. While I finish up school, I am going to plan vacations to states and try and get a feel for the cities/towns.

For a little more background:

• I lean slightly more red but it doesn't matter too much
• Currently in NYC I rely only on public transit but know I'd have to drive anywhere else
  
• I lived in Richmond, VA for a time and thought the driving situation seemed fine
• I plan on having kids
• COL is important
• I'd like a suburban situation more than being isolated rural
• Right now I have a tight circle of highschool friends I game with online just about every day and am content. I also wouldn't mind being friends with a neighbor or community members
• I have mild to severe eczema and seasonal allergies, so I'd like somewhere that isn't hot all the time. I constantly run hot and sweating irritates my skin more. Because of this, I'd also like access to a good doctor to continue treating my allergies and eczema.
• Having decent American diner food or Italian would be nice as well.

So one of the main places I've been looking at is New Hampshire. Everything I've been finding out about NH seems perfect to me. I've looked up entry level accounting and elementary school positions on Indeed. Starting salaries for us would be around 40-60k & 35-50k respectively.

Rent seems though to be going up in NH and getting close to NYC prices. Does NH seem like it'd be a good fit for me? If not what other states should I really be looking at? I have heard a lot of Colorado, Ohio and Michigan as places to consider as well. Any advice or suggestions are appreciated!