Visting friends in Prague - where to go from there?

When you love Italy, why not again? Personally I am very charmed by Bologna. Interesting city without the tourist crowds of Florence or Rome. Good base for daytrips to towns around, like Ravenna and Ferrara. A little bit further afield Mantua and Parma are well worth a visit.
I checked for a random date in September and found a direct flight from Prague on CSA at a most affordable price.

You can certainly fly to Italy, easier and usually cheaper than 12+ hours on the train, or other areas (France, Spain, Scandinavia) will be similarly accessible. Try www.skyscanner.com as an airline search engine.

If you wanted to head toward Germany, Austria, or Hungary, for instance, then ground connections are pretty easy; see the DB link at How to Look Up Train Schedules and Routes Online. Rick’s Train Travel Time & cost Map gives you an overview of faster train travel times in hours, as well as regular (full-price) 2nd-class fares.

If you're already in Prague, why not see the rest of the Czech Republic instead of heading elsewhere? If you're not interested in the Czech Republic, what about any of the adjoining countries - Poland, Germany, Slovakia, Austria?

Prague is not that far by car to the Dolomites in Italy - about 7 hours or so. If you haven't been to this area it's well worth it. We have friends in Prague and they ski there on weekends during the winter. The mountains there are some of the best in the Alps and are beautiful in all seasons!
From there you can drive down to Verona and Milan, just a couple hours further over the mountains.

Vienna and Budapest, or Salzburg and Munich are two easy alternatives possible by train from Prague that come to mind.

Prague to Dresden to Berlin. or Prague to Vienna to Budapest (classic trip). Why not see something completely different? There are excellent high-speed rail connections.

You can reach almost every place in Europe within three hours from Prague, so: what are your interests?