A bit late replying, but I can relate myself (I like classical piano music and like listening to Classic FM). Classic FM produce a CD called 'Piano Favourites' which I bought and was quite a nice general introduction into finding the sort of composers I'd like to listen more of. It's mainly the more popular pieces (e.g. Gymnopédie No. 1, Clair de Lune, etc) but I found it to be a good introduction.

Chopin's Nocturnes are my absolute favourite collection of piano music - especially Nocturne No. 2 in E Flat which is probably my single favourite piece of music. If you like concertos with an orchestral backing as well - which might be less relaxing but certainly no less beautiful - I'd definitely recommend checking out Rachmaninov's four piano concertos which are brilliant. Beethoven's piano sonatas are well known but worth checking out - you've probably heard the more famous bits (e.g. Moonlight Sonata), but the other pieces are sadly overlooked.