Where I always see the big cost of living discussion is around housing. That is what I would look into. Will your monthly mortgage and/or rent be enough to offset the lower wages?
that DOES seem to be the biggest factor in c.o.l. determinations but when we moved from one state to another we tried to look at ALL our normal expenses to see what the difference would be-
property taxes
homeowners/auto insurance (can GREATLY vary area to area let alone state to state)
car registration (HUGE differences between different states)
utilities (12 years after moving from california, despite moving to a place with snow and temps in the negatives all winter, i am still paying less per month than i did in california dating back to the 1990's b/c of lower rates)
income taxes-we moved to a state that doesn't have it

but if considering a move to one that does i would look to see what the rates are like. along the same lines-state benefits. in california there was state disability insurance that was covered through a small payroll deduction. when we moved to washington they had no similar program so a cost consideration was a long term disability policy
sales tax-it's higher than what we had previously paid but it's offset by lower cost on most taxed items. the state adjacent to us taxes groceries though which for me would not be desirable since it's one of our biggest expenditures on a yearly basis
cost to commute-gas prices, tolls, public transportation. is free parking the norm w/employers or do employees have to pay (fairly common here depending on the type of job)?
stuff that isn't a necessity but you consider part of your lifestyle-
drinking/smoking-we have sin taxes that cause people to go to the adjacent state (at $3.77 per litre PLUS 20.5% for alcohol and $3.52 per pack on cigarettes it's worth the drive),
personal 'upkeep'-hair, nails, massages, dry cleaning are tremendously less expensive unless you move to an area w/few providers which drives up the cost,
sports/hobbies/entertainment-if you are into a specific one research how much it costs to do where you are considering moving to. golf here is less expensive than other areas but that's b/c we have lots of courses. figure out if your liesure enjoyments can be met in a new area or if you will have to travel to access them (entailing more expenses).
good luck with your research.