Cost of living (COL) is one thing... quality of life (QOL) is another. I moved from Colorado to Chicago. I did that because the pay was better and it seemed that the COL was about equivalent based on a number of online COL calculators. What one realizes when one gets here is that the COL for the same QOL is actually quite a bit higher. Now, I feel like I came out ahead, but not as far ahead as I had imagined.
Here's the deal: the COL is based on the average cost of housing, food, energy, transportation, taxes, etc; the stuff that makes up the average household budget. Housing and taxes typically account for the largest factors in COL differences. For Chicago, housing prices includes some real hell-holes, where the likelihood of getting shot is higher than some places in the world we consider war zones. This accounts for a surprisingly large part of the city's south and west sides. Buying a home in a "safe" part of the city is rather expensive, or one lives way out in the suburbs and spends hours and $$$ commuting each day. Overall, the average quality of life for the same income in Chicago is much lower.
So, if you consider moving for money, take into account not just COL but also QOL.
I have yet to see an online COL calculator take both into account. If you know of one, post a link.