I have been teaching English legally in Prague, Czech Republic for almost a year and a half, and the experience has been really positive so far. I took a TEFL course through http://www.teflworldwideprague.com
, and started working immediately after. My school helped me acquire a visa, and though the process is a little annoying, it is definitely possible. Based on what my "newbie" friends have told me it is getting harder, but as long as you have the support of your language school or a visa company and apply within 90 days of entering the country, you should be good to go. Most countries in Eastern Europe still seem open to letting Americans work there legally. There are many jobs available in these countries for teaching adults as well. (At least I know in the CR there are anyways, not so sure about the other countries.)
As far as which TEFL course to take, the main qualifications for a legit TEFL course are that it is at least 120 hours and includes 6-8 hours of teaching practice. I really enjoyed my course and found that it prepared me well when it came to transfering what I learned in the course, to an actual classroom. My biggest recommendation is to find a course in the country you would like to teach in, and take it there. The reason for this is that the TEFL school should have contacts with language schools throughout the country, which will prove invalauble when it comes time for the job search. My school had a job fair on the last day of the course, in which reps from 12 different language schools came in and gave information, accepted CVs and set up interviews. Through that, I found a job that I started the next week. Without that help, I would have felt lost and overwhelmed when trying to find a job. They also provide us an extensive network of schools and contacts worldwide that we are welcome to ask for at anytime. (In other words, make sure your school also has valid job guidance, it is so much easier than trying to do it on your own.)
Also, in my personal experience and that of many of my friends, when you settle down in a foregin country for a month to take a tefl course it quickly becomes "home," and it is really difficult to pick up and leave at the end of the course. I never planned to stay in Prague beyond the course, but I fell in love with it and cannot imagine leaving anytime soon. I love everything about my life here. I work for one of the larger schools in Prague teaching business English to adults, and I really enjoy it. The students are a lot of fun, and have given me an "insider's view" of life in Prague that has enabled me to appreciate what I'm experiencing so much more.
Overall, my advice would be to pick your country and go for it! Teaching English in a foreign country is a lot of fun, and it has expanded my views and changed my life in so many ways. I came right after I finished grad school (I have a masters degree in School Counseling,) and haven't looked back since. Life abroad is addicting, I don't imagine I'll be moving home anytime soon!