I'm always touched by Medtner's "Alla Reminiscenza." It makes a great encore piece.
(Did you know tchaikovsky has a piano concerto No. 2? I bet you didn't!) I've never heard it though
He also has a fragmentary piano concerto no. 3
I really do believe that the most sublime, touching, beautiful melody is the adagio from Mozart's clarinet concerto. Whenever I'm anxious, nervous, scared, etc etc I listen to it and all my tensions ease away. It's so relaxed and beautiful... I can't really describe it. Definitely the most beautiful thing ever written, IMHO.
Mozart actually has countless slow movements that are sublime beyond words ...... especially those in his piano concerti.