There are certainly many areas that will provide a home in the price range that you seek.
Just out of curiousity, Paul, what drives you from Colorado to NY, with full understanding that it's absolutely no one's business but your own? I completely understand a response that indicates as much, but I just have to ask.

Paul,
You emailed me sometime ago to let you know if I heard of any great homes in the woods in NY for you.
I cannot find your email as I lost some of my files after having to re-install Windows. I have just heard about a great newer log home close to your range with a pool and 2 car garage for you in a safe area on a private road in a quiet community in Upstate NY about 2 hours from NYC city that is also accessible by train. Please contact me again! Also anyone who is interested!

Paul,
Many areas in NY state are beautiful and wooded and safe... Ulster, Delaware, Green and Sullivan and Orange counties have wooded areas that aren't that far from Manhattan..Further away the "Adirondacks" are lengendary and spectacular. Please feel free to email me or check back for a link to my new broker affiliation and I would be glad to refer you to someone who is an expert in those areas of New York State

Hi Paul, you might want to look in Dutchess County. Maybe Wingdale, Dover or Amenia. All these towns are on the Harlem Valley Train Line to Grand Central (NYC). A lot of the land is still farmed, and there are beautiful lakes. Should you need more info, please do not hesitate to e-mail me back.
Good luck, Elisabetta