Chopin's Prelude in C# minor, Op. 45 is a beautiful piece that isn't hackneyed (yet).
MacDowell's 'To a Wild Rose' is simple yet poignant.
Barber's Nocturne Op. 33 (I think, it's 30-something) is a lovely and atmospheric, almost haunting.
The Barber and Chopin pieces both have short cadenzas that can be a little tricky at first but they aren't too hard to pick up. The MacDowell is easy.