Well, I went the opposite way, from the midwest to Seattle.
I did a few calculations on my own. First was the cost of living index. So say the COLI was 0.85 where I was from, and Seattle is 1.05 (making these up)- I needed a 24% bump in salary to "make the same". However, I'd also be saving two fold - one was because of no state income taxes, so I'd be saving almost 10% by moving to state without. Also, since Seattle has great public schools, I'd "save" 20k/year by not having to have our kiddo in private school. However, housing costs added a separate bump in my mind- since living close to my work included an extra % in housing cost above and beyond the COLI, I added in extra to that.
So I came up with a minimum move number. Luckily, they met that number (actually, it was well over) and I accepted the position and moved here. And we've made lots of money ever since.
In your position, it's slightly opposite. Sounds like a more challenging role for ultimately less money but also a much lower COL. You'd have to figure out what the minimum you'd be willing to work for. Using your currently salary might be difficult because of the Seattle premium. But you could figure out what your new budget might be like there. Also what is the total package? What about retirement contributions, sick leave, vacation days, etc? Can you negotiate a work-from-home once a week? Etc? Whatever it is that you personally value, it might be easier to negotiate some of those things rather than baseline salary.
Also, make sure you get several days to interview or tour the new area if you don't know it already. Make sure you really want to live there and see what the culture is like. Go visit parks, a grocery store, some of the "touristy?" things people do. If you're moving from Seattle, you probably value outdoors, liberalness, and access to really great museums and activities (I'm totally generalizing but oh well). Make sure you'll be happy with your transition and good luck!