Dear Bill:
The list of 20th-century composers of piano music is very long. Also it depends much on personal taste, since there's no common language. Anyway, let me make some suggestions:
- Italy: Dallapicolla, Ghedini, Castelnuovo-Tedesco, Berio, Aldo Clementi, Donatoni, Petrassi, Scelsi, Togni, Federico Ermirio;
- France & Spain: Milhaud, Poulenc, Satie, Messiaen, Boulez; Mompou, Turina;
- Great Britain: Bennett, Berkeley, Britten, Maxwell Davies, Ferneyhough, Tippett, Dillon;
- German & Austria: Hindemith, Stockhausen, Werner Henze, Lachenmann, Rihm; Schoenberg, Webern, Berg, Krenek;
- Eastern Europe: Bartok, Enescu, Martinu, Szymanowski, Tansman, Gorecki, Raubenstock-Ramati, Lutoslawski, Kurtag, Ligeti, Xenakis;
- Scandinavia: Rautavaara, Edlund, Abrahamsen, Borup Jorgensen, Ruders;
- Russia, former CCCP, etc: Myaskovsky, Prokofiev, Rachmaninoff, Shostakovich, Stravinsky, Part, Schnittke, Ustvolskaya, Kabalevsky;
- North America: Barber, Copland, Cowell, Gerswhin, Ives, Babbitt, Cage, Carter, Rorem, Feldman, Chavez, Ardevol;
- South America: Villa-Lobos, Camargo Guarnieri, Mignone, Nobre, Gnatalli, Ginastera, Kagel, Piazzolla, Santorsola;
- Asia, Africa: Takemitsu, Volans.
Oh, boy...the list is endless. I just quote the composers I like the most, and I'm sure that I forget some of them. There are many many others: it's just a matter of time to listen. And to play!
If you need any further help, please let me know. Best wishes!