Travel to Prague, Budapest, Vienna or London

3 weeks would be plenty of time. 2 weeks would be rushing it especially if you wanted to get a flavor for it. If you have never been to Europe before I would start in London, but all the cities that you are traveling to are easy to navigate and find your way around.

I would say that you need a good solid week in London alone. You can get by on about 5 days, but London is huge and there is A LOT to see. My husband is from there and I've been several times in the last few years and I still feel like a week isn't enough time. I would go to London first. Budapest and Prague are each a 3-4 day visit. I haven't been to Vienna yet (going next month actually), but it looks like 2 or 3 days would do it, depending on when you go. I am sort of kicking myself for scheduling the trip in August because there isn't a lot "on" during that time frame. One advantage to going to London first is that you would have to go there anyway to transfer planes if you are coming from the US. Then you can fly once to any of the other cities and buy a "European East" pass from Rail Europe and make a loop out of visiting them. It's $299 for 5 days of first class or $209 for 5 days of second class, plus the train reservations, which add about $20 to each segment of travel. It's 7.5 hours between Prague and Budapest, 3 hours between Budapest and Vienna (although you can also do a 1 day layover in Bratislava which is about halfway), and 4.5 hours between Vienna and Prague. Hope you have a great trip!