Maybe chain stores like Fujiya or Cozy Corner? They're both basically cake shops, but they have gifts and things that last longer.
Also, in my experience, the really big supermarkets - the ones in the Aeon Malls - often have a separate sweets shop within the supermarket with beautifully packaged chocolates etc.
If you're after wagashi (more traditional sweets) then there are stores everywhere. Akasaka Mochi has beautifully packaged mochi type sweets.