A bit of research will reveal that there are an astonishing large number of countries you can buy your way into. However, they’re either not in Europe or, like Austria’s 3,000,000 Euro investment program, prohibitively expensive.
Enter Latvia. Latvia is a small country on the Western border of Russia and it's a member of the European Union. As a way to help boost their economy, the Latvian government passed a law in 2010 to allow people to gain residency for a real estate purchase or investment in business. I'll focus on the former as that gives you a place to live along with residency.
Latvian immigration law allows non-Europeans to purchase Latvian property worth 72000 Latvian lats (~103,400 euro or 133,400 USD) outside of major cities, or 150,000 lats (215,400 euro or 277,800 USD) inside of Riga and other major cities. With that and a background check (immigration authorities are keen on keeping out criminals), you can get a residency permit for five years. I've read the Latvian nationality law (English PDF) and it appears that most people will then be able to apply for citizenship in Latvia, though you'll need to speak the language, know the history, etc.
In short: if you have some spare cash, Europe is waiting for you.
This Latvian immigration scheme is unpopular with some Latvians, though most of my research suggests that this unpopularity is aimed at Russian immigrants due to a rather understandable fear of Russian influence in Latvia. Others are concerned about those who are heading to Latvia solely as a means to enter Europe and have no interest in the country itself. There are fears that this will drive up Latvian housing prices to an unaffordable level, though the market was moribund prior to this law. Here's a BBC video about the topic.
Having lived in multiple countries, I am very familiar with this concern about those who do not integrate, but it’s often an abstract concern: once you start to learn the language and get to know your neighbors, people everywhere tend to be friendly.
A word of caution: like any international move, this one has some major caveats. The Latvian economy is struggling and this residency scheme does not give you the right to work in Latvia (though you can bring your spouse and children). It also has the unfortunate habit of being a crossroads for various wars between neighboring countries. That being said, Lonely Planet seems quite keen on Latvia and, truth be told, if they're far enough down, perhaps the only way they can go is up?