I take it you are planning to visit Berlin for a week after your conference in Prague? Where does Budapest come in?

Many of the responses seem to think you are heading directly to Berlin, but their thoughts are right in that you should plan on a night back in Prague if doing anything other than flying -- and if you are flying and play to return to the US the same day, plan for a longer layover -- 3-4 hours. Since you would be buying separate tickets if a delay on the BER-PRG flight causes you to miss your PRG-USA flight you likely in some trouble as the US bound airline will treat you as a no-show. Depending on your fare class, in theory they could make you buy a one way walk up ticket. (Do some online searching and you'll see lots of horror stories of people on cruises with flights home the day the cruise ends only to have the cruise ship arrive late)

I echo those that suggest taking the train. I found my Berlin - Prague train ride very interesting and educational. Of course, it was in Jan 1990 so it doesn't really apply to today