In general, anywhere in Europe is a bad idea for someone from the US if you want to cut costs. The dollar's at an all time low of $1.52 to the Euro today.
I moved to France two years ago. I did it just for the experience while contracting with companies in the US. If you work for a company here, then the Euro rate won't be so bad. That said, you'll have to get used to a much lower rate than people in our line of work are accustomed to. Of course, if you're reading YC--especially this post--then this isn't really a consideration.
Europe has the Schengen Agreement, which allows people from the US (and other participant nations) an automatic visa to stay for 3 months. Anything beyond that takes an enormous amount of time and red tape.
Getting a place to stay is very difficult for a foreigner. First, you have to get a bank account, which is difficult. They want 10's of K Euro and often several K frozen in case you have an overdraft, which is regarded very severely.
Once you have your bank account, you need to prepare a dossier for the real estate person to pour over. That will involve three years of tax returns, your bank accounts, letters from employers, etc. Most landlords require a personal guarantor--someone who will pay the rent if you don't. And that's for the natives! If you don't have a company to do that for you, well...I guess we got lucky (a big deposit probably helped). This is probably because it's common for people to stop paying when it cools off. There's a law that makes it illegal to evict during the cold season. The leases here are three years. Landlords can't terminate it and you can't break it without significant cause.
There are other things to consider, such as the driver's license. Mass transit is great near Paris. Otherwise, you'll probably need one. You have a year on the US DL. If you're from one of the small states with a specific agreement with the French government, you can exchange. For the rest, it's very costly and difficult. Hoops include mandatory drivers school at several K Euro. The test takes almost 1K. Retakes cost as well. There is no English option. Questions are timed (unlike most/all of the US). Sometimes no answer is correct, sometimes multiple answers are correct. Examiners try to trick you or trip you up on technicalities.
France definitely is the most difficult. Most other European countries are a little easier along one dimension or another. Regardless, though, the Euro/Dollar conversion is punishing.