Renting vs buying doesn't affect the stash you will need. After all, you will use the total cost of living per month/year to calculate the stash you have. For a renter this amount will include rent, for a homeowner this will include mortgage, maintenance, taxes and insurance.
If you are interested in retiring to a place you've never lived before or haven't lived for a long time, I would definitely want to experience living there before I pull the trigger, because if you FIRE with only enough money to live in the LCOL area, and you end up not being happy there, it's not easy to go back to your pre-FIRE life in the HCOL area to save up some extra money. How badly do you want to FIRE? Are you totally unhappy in your job and completely burned out
Even if I was planning to relocate to a LCOL area after retirement, I'd still like to have a stash high enough to allow me to live in a MCOL area, for several reasons:
- you might want to move to another area at some point and with a lower stash, your options are limited
- LCOL areas are cheap, but this comes with a price tag: often the job market isn't that great and the available services are limited.
At some point you might want to work again in some capacity or need certain services (like specialist medical care) that aren't available where you plan to live.
- if you aren't planning to ever work for money again, it's especially important that your stash is high enough, because life might throw a few unexpected emergencies at you that cost money from your stash. If you can just about pay your bills following the 4% rule (a barebones FIRE) then an unexpected emergency could negatively affect your income permanently.