Insurance issues

I have read some on here about people's situations but I am so new to having to deal with health insurance besides the basics. It was recommended that I go to the Chiari Institute in New York; however, when I called my insurance company today (I am in Florida) they said they on not in-network. I asked if there were any other options besides paying it all out of pocket and I was told no. I am wondering if anyone else has had these issues? Is it worth calling the institute and talking to their people? I asked about an appeal process and the guy said that from what he knew unless the doctors there were the only ones who could do my surgery, the insurance would never go for it.

Any advice would be greatly appreciated!