ok you're doing the search I'm doing with the exception of house size. A couple questions for you.
Are you going to need work or are you self supporting?
Do you need alot of civilization?
If the answer to the second question is yes, then I recomend the area around Ithaca and Cayuga lake. But expect that area to be very expensive for anything decent. Also the area is building up fast. I personally don't care to be around any of the fingerlakes. The area is pretty much overpriced. And regulations are getting outrageous as the area explodes population wise.
The area around Allegany and Cattaraugus counties are the area I like. Places are cheap, but, there is little work in the area. There are blue collar job, but more people than jobs so wages are low. I really like the area around Cuba, NY and Olean, NY. They are nice clean medium sized towns, and the surrounding countryside is very reasonable. Wellsville is a strange town and kind of depressed. Depressed enough that they are throwing development around without thought, just to have it. Twenty years ago I loved Wellsville, now I steer as far around it as possible.
If you don't mind being within an hours drive of a big city, Niagara county is an area that is still very rural. Same with the western half of Orleans county. If you look in that direction watch for bad drainage north of route 104. The area is really flat and there is usually a hardpan not far down. I'm north of 104 in Monroe county and my garden can't be tilled until memorial day due to the bad drainage. It's something important to consider. If it were me and I wanted to stay near the big lakes, it would be the area around Newfane/Olcott/Wilson/Appleton. Nice little towns, no jobs though. A determined commuter could do the Niagara Falls, Buffalo, Rochester commute though. And those cities have decent jobs.
There was an interesting place in Dansville about 45 minutes south of Rochester on realtor.com, I'll see if I can find it for you. If it's still listed, I'll post the link.
My search as of this weekend is a 25 mile radius around Bradford PA. I fear saying this here. I don't want everyone heading there driving up prices. :no: If you'll consider PA, look at McKean county. Land there is 1/2 the cost of NY and 1/4 the taxes. I've fallen in love with the area. My 25 mile radius lets me include Cuba and Olean in my search.
Now, my experience with United country and Realtor.com is that a piece of property listed with them will be 10-25% more expensive than places not listed online with big websites. The best way to search what you want is to go drive around and pick an area you like. Then stop at a little grocery store and get yourself the local pennysaver or county advertiser. If you find a area you really like, stop and make some friends and ask around. For example, I was down in PA saturday visiting friends I made online. The husband took me for a ride out in the hills. How does a 2 bedroom ranch house 20 years old on 44 acres for the price of $53k sound. Nope don't look for it, it's not listed with a realtor, and it won't be. And from my past year looking. I could put you in a decent old farm house on a few acres for under $30k easy in McKean county. Oh and the property taxes down there will run $400-600 a year. Unlike NY where taxes seem to start at $1,000 and go up quick.
lol, I'll get down now

and go find you the link for the place in Dansville.