Route planned now what to see

There is too much to see. So you have to decide how long you stay in each destination. Rick Steves has guidebooks for all of your destinations. It's perfect for you. For example: if you have two days in Prague see this and that. If you have three days you can add this. With four days you add another sights and so on. Unlike other guide books he is practically doing your itinerary for you.

Not that it's something you need to book in advance, but you should do some walking / bike tours. There are some good ones in Amsterdam and Berlin in particular.

Check out Prague for the opera. We saw Don Giovanni at the Estates Theater (where Mozart debuted it). We got a center box, front row seats, with the best views of the entire place.. for $72 (for 2 people). I can't even see a local Broadway show here for $70 for one person! There are tons of just as good, but cheaper seats as well.. but it was for my birthday so we splurged.

This is the official website (they also have another gorgeous theater with shows, but we loved the idea of the last theater standing that Mozart conducted in and where he debuted Don Giovanni) - http://www.narodni-divadlo.cz/en

Budapest: Tell me what date you arrive and what date you leave and what part of town you are staying in and I will look and see what is goin going on in town.

I too would suggest Prague for Opera or classical music .
http://www.bohemiaticket.cz/
this website is pretty good for letting you know what is on. I am in Prague several times a year and often go to shows,I too have been to see Don Giovanni at the Estates, prices are a fraction of what you pay in other major cities.
I would not worry about booking much for Prague unless there is something special you want to see,I have seldom had a problem getting entrance or tickets to places I visit.I am back in the city in early August .