First of all, I am NOT an expert by any means in this area of discussion, and have no relevant professional and/or full-time experience in IR. My limited experience with (graduate) IR schools has been only through my application process for entry in the Fall of 2012, and I applied to 10 IR programs, 4 in the UK (LSE, Oxford, Cambridge, Durham), 5 in the US (American, Fletcher, GWU, BU, DU), and only 1 in continental Europe (IHEID). I was moderately successful with a total of 6 acceptances out of 11 (SOAS for MidEast Studies is the one not included as IR), and will be going to LSE this fall.
That said, I considered applying to some other schools in continental Europe, like St. Gallen (SUI), and Sciences Po, but ended up not applying to St Gallen because it was the German part of SUI even though it was taught in English, and Sciences Po because it is partially in French (have nothing against German or French, just have no grasp of either and applied to a lot of programs as well).
As for other schools, I've heard of a few others being good, but have not investigated most that much for myself: College of Europe, SAIS Bologna, Leiden, Groningen, Clingendael-Hague, U Geneva, Geneva School of Dip. and IR, CEU Budapest, U Economics Praha. If you're interested in Turkey at all (where I am from originally) though they are not going to be super-well known outside of Turkey and Europe, check out Bogazici (personally studied abroad there), Istanbul U, Middle East Tech. U, Bilkent, Koc, Sabanci.
Another couple of sources you might want to take a look at in your search are first wikipedia's page (List of international relations schools - Wikipedia, the free encyclopedia
), and second APSIA's member and affiliate schools (APSIA.org) as they are supposed to be a credible association of IR schools but have more US members as their requirements for membership tend to favor US schools in some ways.
Also, with your interests, be sure to check out schools with good EU studies or European studies schools, not to mention the best economics or political-economy programs in Europe... Also do not discount the possibility of the politics (political science) masters or PhD focusing on IR or European politics, or public policy/public affairs programs.
Now, as to why the continental schools aren't mentioned as much after the juggernauts of the US and UK, I can only speculate. Perhaps it has something to do with these schools being ones that teach in English (obviously), but also that US and UK universities in general tend to dominate in overall world rankings. Another different approach might be argue that because the United States is such an influential actor in IR and in the world economy, people feel like schools in DC and NYC will give them a solid chance of making it in the professional worlds of traditional state-based IR or IOs, or even the corporate and/or finance sectors. This argument could also be applied to schools in London, Geneva, Belgium, and even the best in China, Russia, Japan and Korea.
I haven't covered some of the differences between the US, UK, and European schools, but it isn't completely generalizable. A few short things I would say is that the US schools tend to have 2 year programs, UK programs tend to be 1 year (more like a calendar year with 3 semesters in American terms), and EU programs vary greatly but many are 2 years (IHEID and St Gallen are to my knowledge 2 years). Also, US programs can tend to be more general in scope and UK/European programs can tend to be more specifically IR-based. Lastly, cost and scholarships are a consideration. US schools seem to have more funding for masters students while UK and EU doesn't give out as much (but with IR masters, I've heard the expectation is that people will go on and make money professionally, so they are expected to use loans, so American programs tend to be more expensive and longer which just adds to expenses for self-funded students).
Sorry for the long reply, but you did ask a lot and I kept on going. Feel free to ask more or clarify if you like. (Btw, I never was a regular here and was much more involved with The Grad Cafe. Disappointed to see no replies from the resident experts here.)