I have a lot of student loans and so I'm looking at least desirable areas with hopes to negotiate a lot of money to pay off debt. I assumed they will pay a lot. I'm a US citizen. I don't have a strong desire to be on the coast or major cities because I know that they will be saturated with psychiatrist and pay well be substantial lower than it would be for the Midwest.
your assumptions are wrong. the midwest is by no means the highest paying part of the country (its on the lower end in $ amount going by the salary surveys), and you cant negotiate a lot of money because psychiatry isn't a priority. the midwest is where psychiatry went to die. also indiana is a tort reform state which means they dont have an incentive to hire psychiatrists. tort reform is actually not good for psychiatrists because we have the lowest rate of lawsuits but those lawsuits (which are usually targeted at institutions) are what have been driving up psychiatrists compensation in certain settings (particular kaiser, VA, corrections). your negotiations failed because you have no leverage and no leg to stand on.
the NE is no good but west coast and mountain west are good bets (WY, MT, UT, ID, CA, WA, OR). WA state might be good, ive seen a bunch of reasonable jobs paying 300k there, and no state income tax. look outside of seattle but the state is beautiful. it used to not pay so well (possibly taking into account lack of state income tax) but pay seems to have gone up over the past year. OR is not bad either and insurances and worker's comp pay well there (the state tax is high tho). CA obviously has its taxes but much of the state is not as expensive as you think once you get out of the most desirable areas. If you work for the counties, they have v. good benefits and may have good loan repayment options in addition to paying over 300k. underserved areas and corrections pay best. there is always kaiser too who will often give you a golden handcuffs. there are contractors that pay well too.
Not sure who has been advising you but recruiters are typically not the way. if they are selling a pile of a turd no negotiating is going to polish a turd into gold. they will spam you with crap.
also in order to negotiate you really need to have decent offers. so you can say well "x is going to do this for me.."etc and pit them against one another. without that you dont have much leverage. you may be fooled by reading these threads that places are so desperate for psychiatrists and get whatever you want. wrong. most jobs out there are terrible which is why they can't fill. there's no shortage of psychiatrists. there are a shortage of psychiatrists willing to put up with this sort of crap. bureacracy and idiocy often win out.
also if you continue to live like a resident and diversify your work (i.e. do a mix of W2 and 1099 contract work) you should easily be able to pay off your loans in a few years. you don't have to move to some hole and move the meat to accomplish that. it's a recipe for burnout. remember that once you're in a certain bracket there are diminishing returns so it may not be in your interest to be making too much money.