I took the train from Prague to Amsterdam, then the ferry back from Rotterdam, just because it seemed the easiest route. The European overnight trains are a pretty slick operation, with parts of trains leaving and joining in different cities, so the train I was on divided and a section went to Copenhagen, and when it arrived in Amsterdam, a new part had joined from Poland.
The last week I spent in Prague pretty much doing tourist things, including the national museum, which has different parts in several locations, including at the National Monument and the former Parliament building. Both are fascinating buildings. The National Monument comprises rooms to honour the war dead and statesmen, and a chamber for inauguration of the Presidents of the inter-war republic. Communists manipulated the presentation of Czechoslovak history, including choosing to honour the Red Army rather than the resistance. Of course, the monument celebrates a country that no longer exists, so preserving it as a museum makes a lot of sense.
The former Parliament has some interesting elements, including the use of suspension for staircases and even parts of the building. They have a large amount of artworks there too which deserve a bit of attention and explanation.
Prague has the least developed cycling facilities of the cities I passed through, although it also seems that some steps are being taken, and there are a few off road paths, including the main national routes. All of the former GDR towns I went through had very good bike routes and plenty of people using them, just as in other German towns. Although Germany may not have reached Dutch levels of cycling it is very common in Hannover, Magdeburg, Dessau, Wittenburg and Dresden.
The Elbe route (I didn't cycle along it all the time) is quite a mixed bag, the surfaces in the German part include a lot of cobbled roads and paths, and a few ill-maintained dykes. This can slow you down a lot. Other parts had GDR concrete tractor-ways or other surfaces which are a bit better for touring bikes. It is of course very meandering as well, following a river as best as it can.
The whole of the route from Dresden to Prague is pretty flat, I did encounter a few mild climbs but nothing more than a few minutes and nothing very tough. It's really very easy cycling.
On the Czech side, they are putting a lot of money into the route, so long stretches are wide, dedicated tarmac bike paths. Other parts are quiet lanes. Only a few parts seemed difficult to ride on. Cycle tourists from Dresden to Prague are extremely common, and the path can be very busy, often with large groups travelling together. Bars and restaurants target them heavily, and you can find it hard to avoid deciding to stop for a beer.
One thing I would maybe do differently is to take a bit more time over the Elbe journey. There's a lot to see, and I didn't have the time I should have given it. So I might go back! Although, I equally wanted to see more of the Czech Republic and central Europe, like Bratislava and Budapest. But that might take a different kind of trip, starting and ending with a train journey.