Here's what goes into a payment:

Principal and interest (this is the loan payment itself)

Property taxes (lenders want you to pay your taxes, so they put this in an escrow account)

Homeowners insurance (lenders want to make sure your home is insured, so they put this in an escrow account)

Mortgage insurance (needed and charged if you put less than 20% down payment)

HOA (not in your mortgage payment, but something you may need to budget for)

So, naturally if your property taxes are higher in a specific state, you'll afford less of a purchase price. The same goes for homeowners insurance.

I'm going to assume a 5% down payment, with a .0025 mortgage insurance factor

Here's the chart

part 1 approximate purchase price for each state

StatePurchase Price
AL$418,701
AK$404,050
AZ$424,799
AR$405,907
CA$417,917
CO$415,570
CT$370,796
DE$425,071
FL$375,686
GA$390,728
HI$444,785
ID$398,629
IL$351,190
IN$397,437
IA$386,088
KS$400,897
KY$399,115
LA$395,125
ME$379,622
MD$368,780
MA$369,417
MI$376,769
MN$378,710
MS$412,287
MO$405,680
MT$409,158
NE$393,693
NV$407,847
NH$384,188
NJ$346,228
NM$411,286
NY$354,720
NC$401,187
ND$405,748
OH$403,851
OK$407,886
OR$399,873
PA$387,236
RI$382,658
SC$401,198
SD$395,727
TN$398,119
TX$381,266
UT$390,751
VT$375,388
VA$385,511
WA$393,396
WV$393,256
WI$375,164
WY$419,563

part 2 side by side with the state's median purchase price

You may be able to afford a higher purchase price in California than Texas, but can you realistically get a house for that price? This shows you if a $3,000 payment is realistic

StatePurchase PriceMedian Home Price
AL$418,701$231,946
AK$404,050$395,096
AZ$424,799$440,228
AR$405,907$219,825
CA$417,917$809,227
CO$415,570$567,724
CT$370,796$465,586
DE$425,071$406,448
FL$375,686$405,280
GA$390,728$338,734
HI$444,785$973,555
ID$398,629$465,288
IL$351,190$292,156
IN$397,437$254,931
IA$386,088$237,357
KS$400,897$242,859
KY$399,115$225,191
LA$395,125$213,371
ME$379,622$413,961
MD$368,780$451,121
MA$369,417$685,886
MI$376,769$259,702
MN$378,710$358,473
MS$412,287$189,849
MO$405,680$264,646
MT$409,158$467,372
NE$393,693$277,389
NV$407,847$472,477
NH$384,188$528,377
NJ$346,228$588,776
NM$411,286$316,778
NY$354,720$487,737
NC$401,187$339,287
ND$405,748$289,622
OH$403,851$246,244
OK$407,886$218,822
OR$399,873$515,474
PA$387,236$286,397
RI$382,658$506,723
SC$401,198$306,512
SD$395,727$321,393
TN$398,119$335,560
TX$381,266$308,212
UT$390,751$546,553
VT$375,388$406,730
VA$385,511$416,516
WA$393,396$626,603
WV$393,256$169,759
WI$375,164$334,636
WY$419,563$367,126

part 3 which states have the most realistic chance of finding a house for a $3,000 monthly payment

Further down on the chart it gets a little tight, meaning the median price is about $50k or less above the amount a $3k payment would get you.

StatePurchase PriceMedian Home Price
WV$393,256$169,759
MS$412,287$189,849
LA$395,125$213,371
OK$407,886$218,822
AR$405,907$219,825
KY$399,115$225,191
AL$418,701$231,946
IA$386,088$237,357
KS$400,897$242,859
OH$403,851$246,244
IN$397,437$254,931
MI$376,769$259,702
MO$405,680$264,646
NE$393,693$277,389
PA$387,236$286,397
ND$405,748$289,622
IL$351,190$292,156
SC$401,198$306,512
TX$381,266$308,212
NM$411,286$316,778
SD$395,727$321,393
WI$375,164$334,636
TN$398,119$335,560
GA$390,728$338,734
NC$401,187$339,287
MN$378,710$358,473
WY$419,563$367,126
AK$404,050$395,096
FL$375,686$405,280
DE$425,071$406,448
VT$375,388$406,730
ME$379,622$413,961
VA$385,511$416,516
AZ$424,799$440,228

Here are the states that didn't make the cut:

Maryland, Idaho, Connecticut, Montana, Nevada, New York, Rhode Island, Oregon, New Hampshire, Utah, Colorado, New Jersey, Washington, Massachusetts, California, Hawaii

I bet there are states here where you could find a $3k mortgage payment, but it just gets a little more difficult in general.

Anyway, hope you found this as interesting as I did!

Sam