[noa]

In terms of where to stay, all I can say is that I suggest trying to stay downtown in both cities. Amsterdam is easy to get around, but its more exciting to stay downtown there. As for Prague, it will be of great benefit in terms of tourist attractions for you to stay downtown. The outer edges of Prague can be harder to navigate, so your stay will be much easier if you're in the heart of the city.
In Amsterdam, I liked a lot of the museums and also the Heineken factory, and of course, the coffee shops.
In Prague, I would recommend going to bars that specialize in certain kinds of beer, like Gambrinus or Budvar. Other than that, check out Old Town Square, Prague Castle, and walk along the river. There are tons of cheap places to eat in Prague, so try to avoid the expensive tourist traps. Finally, one last thing to know about Prague is that you should negotiate the price of a cab ride before you get in. There aren't any meters or fixed rates, so its up to you to agree on a reasonable price if you're gonna ride one.