They are all over. Head over to zillow/redfin (or the corresponding real estate site for your region) to see them. They won't be in the hip city center everyone wants, but choices are plentiful if one is willing to sacrifice a few wishlist items.
"Cheap" is of course relative the the region/country so actual numbers will vary. I'm in California so I can give a California-centric answer.
Browsing zillow I see over 30 condo (and a few house) units for less than 200K in the Sacramento areas (not exactly the boonies, it's the state capital).
In the Fresno area I see around 60 units (many houses) under 200K. Some friends moved to Fresno and they have a very nice place, for pennies on the dollar compared to San Francisco.
For those who don't want a big city, head north of Sacramento towards Oregon and tons of choices to work remote and buy a place cheap.
Mind you, I set the search limit to <200K, but that's extremely cheap by California standards. Even 25 years ago 200K was a cheap house in California. If you increase the search criteria to a more reasonable 300-400K there are way more choices and areas.
Or, to put it simply, move out of the big city, and the prices drop by a factor of two or more.
Like, sure, a 120sqm house might be 400k in Hamburg and only 230k 60 minutes out to the north west (both needing an additional 25-50% of price in renovation costs), but the average net income is 30k/year and you're expected to have at least 20% in cash.
You can get very cheap houses in Saxony or Mecklenburg-Vorpommern, but there will be little to no infrastructure (like, the next gynaecologist might be a 60 minute car trip away), your neighbors will be down on their luck, unemployed and voting far right, and you'll essentially need to rebuild the house - and you'll need to do much of it yourself because the tradesmen work on construction sites in the big cities and rarely take local jobs.
My main issue would be being more socially isolated as all of our local friends are in Berlin, kids having to adapt to new school/kindergarten (& find new friends), new work for my wife who doesn't work remote (but can find work relatively easily)...It's not impossible but it really sucks that we'd have to leave the city if we want a slightly bigger home (we've 2 kids who share a room & our apartment is in general feeling a bit small for a family of 4).
Without a large windfall I don't think we'll ever be able to afford buying a 3+ bedroom (4+ rooms as Germans count it) home in Berlin & rent would be high enough that no landlord will want us with our current income.
I had hoped that remote work would relieve some of that pressure, but maybe it'll take a generation because many couples can't move anywhere because only one of them can work remotely, or because they don't want to uproot their kids. Not to mention that you'll still need a solid internet connection to work remotely, and that's still hit and miss if you go more rural. And if nobody wants to move to Saxony, the empty villages there don't really do anything on the supply side.
I wonder if it was because it was easier to upgrade/replace the East German infrastructure & as such it's relatively new/good? Sorta like how nice a lot of the highway network in Poland is, because it was mostly only built in the last couple decades.
BTW Pankow is considered a very nice and desirable (and expensive) part of Berlin to raise a family in :)
You're right about small towns, they're probably a good compromise before looking at villages, but it is a very different life style, so probably not for everyone that currently lives in Berlin or Hamburg by choice. I'm curious how it will develop, and I feel fortunate that my personal preferences align with what's cheaper. I feel for those who desire the hustle and bustle of the inner city.
When you work remotely you may want to move anywhere you want. However, there are other things to consider: https://news.ycombinator.com/item?id=35408256 :)
If you want to be somewhere that feels on the up & up and has cool stuff, Brownsville has a decent amount of engineers for SpaceX and you can go watch launches from a public beach if you get there early enough.