When a songs melody begins in the key of C major it should end in the key of?

The answer to this question is not always simple, however if you want a definite answer, look at the tips below:

If you wanted to end on a perfect cadence, you should modulate to a G major chord and then move down to the tonic chord (C major).

If you wanted to end on a plagal cadence, you would modulate up a fourth to a F major chord and then resolve on a C major chord.

If you wanted to end on am imperfect cadence you simply modulate to the dominant chord (in this case G major) and end there.

Finally, if you wanted to end on an interrupted cadence you modulate from the tonic chord (C major) to the relative minor, an A minor chord.

So in most cases a song which began in C major should end in the tonic key (C major), however a song in C major can end in G major (an imperfect cadence) or in A minor (an interrupted cadence).

Hope this helps.