Say you are working in a HCOL area (e.g. San Francisco) with a decent salary. However, in order to buy a house, you'll still have to work for a long time. If you move to a LCOL area (e.g. Minneapolis), your savings would enable you to buy a house in cash. However, you'll have fewer job opportunities in your field. Would you make this move? If you made this kind of move and regret it, I'm curious why.
I think the key part is to have friends and family near the low cost of living place. Picking a city based on a magazine ranking or a spreadsheet doesn't work.
Your financial and life situation are key to this. If you are single, the cost of a shared apartment isn't necessarily worth the trade-offs. If you are starting a family, you want space and being away from bars and nightlife is a plus. Also factor in your savings and asset base. If you have a good amount saved after buying a primary residence, go for it. If you don't have much saved and just paid off student loans, maybe try to work a bit longer in a high cost of living area and try to save a bit more before the transition.
I agree completely with what Eric says above, but I think you also need to consider your job prospects. Some jobs have no issues moving to small cities or rural areas - i.e. work from home, I.T., accounting, etc. You need to consider how financially stable is the company you are moving there for if there are lower prospects for a new job if that company fails or has layoffs. Are you confident enough that you could find another job within a certain time frame that you need.
Tanya at Busget and The Beach moved from LA to Boise and regretted it. She moved back within a year and she wrote some posts.
I'll be moving from a LCOL to HCOL this year. I'll be honest when I say I'm scared.