Good challenges for beginning composers are doing things like:
Choose five notes out of the total twelve. (i.e. A, C#, D#, F, F#) The five notes you choose are the ONLY notes you can use in the entire song. You may use them in any octave, but that's it. And don't make it easy on yourself by choosing five notes that compliment each other well. Or, you could use that as a test. This forces you to be more creative in your writing as there are very few consonant chords you can use to base your music off of. So it's good for melody-building and it's a nice way to learn how to write dissonant music
Or try writing a song using only two odd time signatures. 5/4 and 7/8 would be fun, and with a strong pulse and a good hemiola, they would compliment each other well.