I would personally opt for the master's program in Europe.
Depending on the city you study in it costs approx. 1200 USD/800 EUR per month to do masters in Europe, so your money could last you for about a year and a few months. But if you are willing to live frugal and pick a relatively cheap place to study in you can make your money last much longer. (Tip: Avoid London and Paris like the plague.) Plus you can get a part-time work permit as a student. With the part-time work permit it will not be impossible to stretch your money to last 2 years.
A lot of it depends upon the exchange rate, when the USD was 1,20 to 1 EUR 17k equaled an income of 590 EUR per month. Nowadays the exchange rate is 1.56 to 1 EUR and 17k equal 454 EUR per month. A difference of over 3200 EUR in total!
For a student in a master's program there are also a bunch of scholarships available, look into it.
The main advantage to doing a degree in Europe as compared to the other options are the following:
In a number of European countries there are no tuition fees. Your only expenses are your cost of living.
Doing a degree in Europe gets you the most for your money. You get a degree and you get to spent a lot of time abroad, far more time than on a holiday or by studying abroad for a semester.
And the final advantage: In most EU countries graduating from uni is the easiest way to a long-term residency and work permit in this country. Graduates are given a certain timeframe to find a job suitable to their qualifications, if they manage they will be given a work permit which is otherwise very hard to come by.
So just in case that once your money is gone and you decide you want to stay in Europe because you like it, doing masters in Europe is the only way to go about it.
And if you want to compare that to the cost of a super-low budget trip around Europe: Most tourists need at least 50 EUR per day and person to survive (= not starving and no need to sleep on the sidewalk), which sums up to roughly 2400 USD per month. The majority of tourists use much more though, spending around 3500-4000 USD per month when travelling around Europe. At this rate your money won't last long and it would really be better spent doing masters. BTW, as a tourist you are limited to a stay of 90 days inside the Schengen area.
For Masters in International Business look into the course offered by the HU Berlin. http://www.mastersprogram.de/
http://www.mastersprogram.de/root/en/study_at_hu/costs
http://www.daad.de/
http://www.hochschulkompass.de/
Feel free to contact me for more info, when I was at uni I used to be a guide and mentor for foreign students who had just arrived in Germany or where planning to come to Germany so I know a lot about the paperwork and the rules involved.