There are a lot of cost of living calculators around that will tell you that you Boston is 66% more expensive than Birmingham, which would say you need 191k. However, in my experience calculators like these break down for higher income people like yourself.

If you aren’t spending all of your salary, not all of your salary needs to be multiplied by the % change in COL.

It will depend on your personal finances, but I bet you will end up with more savings making 150-160 here than you were making 115 in AL. Your house will be smaller here, but a lot of other things (including schools) will be much nicer.