NIRVANA. We all are looking for that one perfect spot! I guess it's possible if you have enough money. I can't seem to find that number.
Here we go. I'm about to make a lot of general assumptions and generalizations are rarely true. You'll have to roll this around to see if what I'm about to offer has any value.
I think I got this right, about your location TT. Upstate NY, right? I hope. I dropped at point at Ithaca. The red circle on the map is a straight-line 425 mile radius. That makes driving distance somewhere between 550 and 675 miles depending on the twists and turns. I'm assuming you might want to be within a "reasonable" drive of family and friends.
You can see what states are in the target, but I'd forget about states and politics. Let's not go there, or make it the final consideration.
Within a state you see counties. The population density is illustrated by color. The counties colored shades of gray to black are what I consider suburban / urban areas - population densities over 150 people per square mile. The darker the gray the higher the population. The greens are lower population density counties. The lighter the green the lower the number of people per square mile. The red counties (no politics here) are the lowest densities to the point where there's nobody there and nothing in the way services you might need (an assertion on my part).
I don't know if I need to go further? As you go one way you gain somethings and lose others.
What comes out of this for me, considering your criteria and spinning it to what I know and think I know (!) -
1. One of the most rural areas on the east coast I learned when I was 12-years old still applies. It's bordered on the south by I-80 and on the north by - I don't know what it's called now - The Southern Tier Expressway? On the west by US 219 (memory fails me), and of the east by US 15. It's cold and lonely there. I spent a year there one month. I love JUN - SEP! And there are spots with great deer hunting - and others not so much.
2. Although I would probably never live in WV (I've looked at land there, to confess) all those southern counties in the state have some appeal. Those two red counties you could probably buy cheap land, but it's nearly vertical.
3. In Ohio, just across the WV border along the Ohio River there are those green counties that are interesting. I've looked at land there. It's the right kind of mixed of land uses great for deer and deer hunting. Its rolling down the west slope of the Appalachians with places flat enough for decent ag production, but doesn't carry prime ag land prices. Still, I think you might be looking at a minimum of $3k per acres. Once you get much west of there it's corn/'bean ground and good luck finding land for less the $5,000 to $7,500 an acre for tillable acreage.
4. The circle hits it's southern tangent in central Virginia. Most everything inside the circle is extremely pricey. There's money and opportunity - and taxes. But if you slide south it's an entirely different world. There are many 150- 180 deer killed just inside and outside that circle in Virginia. We just don't talk about it. A lot of that land is in continuous forest regeneration. I'd guess - just a guess - that 15% of the 'forest' land gets cut every year. Makes for great whitetail habitat.
Good luck!