What about his piano sonata? I have never heard it, but I saw the sheet music for it and it looks HUGE.
If you are referring to the "Grand Sonata", op.37, I find it rather perfunctory and nationalistic, particularly with the first movement, which is full of impetuous chords "on the march". After that there are some nice sections that divert away from the 1st movement; the 2nd movement is, at times sole-full with hints of the 1st Piano Concerto. The 3rd movement is more of a scherzo than the score suggests, basically a quick moderato. The short finale is, to me, the most interesting, and requires the most virtuosic skills. Again it incorporates pianistic technique on the level of the 1st Concerto. Overall though, I've never found this sonata to be all that attractive, either for the pianist pondering the learning of it, or the general appreciation of an imaginary audience.
While Tchaikovsky did write some decent solo piano works, it appears to me that the shorter works, as in "The Seasons" (mentioned by others here), tend to be more rewarding on all grounds. Personally I believe he was destined to compose orchestral music with wonderful imagination, and much of the non-orchestral works tend to struggle on their own, for better or worse.
My parents were Classical Romantics, and that's the sort of music I inherited as a child, and while I've embraced far distant "musics" over the years, I continue to appreciate much of Tchaikovsky works. Many people consider it inferior, along with his "successor" Rachmaninoff, but regardless of one's own preferences, just consider the "popular impact" these late 19th - early 20th century composers have had on maintaining a public interest in Classical Music in general. Without a "ground base" of devotes of the most popular classical works, intertwined with "new" (lesser known, yet well deserving of public performance) works, the strength of the platform that much of Classical Music stands on could crumble, and that would be a shameful disaster I hope never to see.
Lontano