Trains get slower and slower the further East you go and Germany mostly upgraded north-south lines. Going from Prague to Frankfurt takes 7 hours vs. under 4h from Paris. Even trains to Berlin or Dresden are slower than trains to Cologne, Brussels or Paris.
So if you want a convenient and fast connection, your only options outside Germany are Brussels, Amsterdam, and Paris (all further West). Vienna or Warsaw are doable and you might also consider Munich or Cologne (North/South rather than East) if that's somehow cheaper but that's about it.
Anything else (Rome, Budapest…) is the kind of things I would actually do because I love overland travel but it's not fast or convenient by any stretch of the imagination.