Hi Sgautr,
I love all of Prague, Budapest and Italy so its a hard decision! All of the places you mentioned will probably be quite expensive once you get there. In my opinion I like Budapest more than Prague – mostly because of the turkish baths in which i could easily lose whole days. Having said that I am glad I have been to Prague and enjoyed it. From Munich you can get easily to Italy with loads of options, including my favourite place – Venice. Have you considered Switzerland? I recommend Gimmelwald in the Bernese Alps. Absolutely breathtaking and most easily reached by an almost vertical cable car.

If those three cities are your only choices … Budapest 100%. Budapest is not expensive at all either. at least if you hostel it. hostels are 20-25 bucks a night, and a beer out wont be more than 2bucks. the baths are great and heroes square is a great place to hangout. They have the terror museum where the nazis and communists tortured locals from the 40’s on. The bath houses are great and nightlife is as good as you make. Im biased though, Im moving to budapest in a month

Well I have to go to Paris, Amsterdam, and Madrid… The question is what to do with a free week in between the Amsterdam and Madrid trips? Is Budapest worth the 20+ hour train ride from Amsterdam to there, and then from there to Madrid?

You could definitely make it out to Budapest in a week, the question is, do you really want to spend at least 2 of your remaining 7 days traveling. Personally, I wouldn’t want to waste that much time. And pretty much anywhere in France or Belgium is en route to Madrid. Obviously these places are more expensive than Eastern Europe, but you can get by on a budget. Then it becomes a question of what you’re looking for.
You can go Loire valley is great for seeing Chateaux, there are tons of places to party and lay on the beach in the South, Dijon is a beautiful Renaissance city and Beaune is nearby where there are several places to do wine tastings (for free, or a small fee). Strasbourg on the German border is a really lovely, fun city. I’ve had a great time on the Cote d’Azur, staying in Menton and taking day trips to Monaco and the Italian border. The beaches are beautiful and there’s quite a bit of nightlife. This fall, I’m planning a trip to Avignon, Arles and Nimes, all of which are full of history (and amazing food). I’d love to go to Carcassonne someday, which is close to Toulouse and Montpelier.

since u are going to madrid from amsterdam….stop midway in paris!