Playing an actual piece is the last stage of testing a piano. You need to do several other tests beforehand - it's probably best to bring a competent technician with you. I always get a kick out of these 'prodigies' who come in and play the fastest piece they have learned to date.
I like going in with several categories to test.ToneVoicingProjectionevenness of note executionevenness of down stroke of one keyweight of actionevenness of action weight across keyboardrepetitionminimum key height for next repetitionfeel of the actionability to sing a melody on topability to sing a melody in the middlequality of bass in harmonic structurelength of note bodybi chord / tri chord breakclarity and fullness of lowest bass notesbriliance of top most notesnon harsh and fullness of sound when playing loudnuance and subtlety when playing softability to change tone color and not just volumecolor the una corda pedal contributesvarious degrees of una corda applicationfluidity in una corda shift mechanisimability to apply nuance with sustain pedalhow well fractional pedaling workseveness of sostenuto letoff tactile surface of keys (does it get slippery with sweat)width of black keys (I like them fat)sound with lid fully up and music rack downease of access to strings for 20th century plucking techniquessoft close fallbaord?does music rack have multiple angles available?
I play the ostinato from Rachmaninoff Bb prelude Op 23 no 2 as loud as I possibly can. This is to see if the piano has an explosive bass. It also tests the weight of the action because you're hitting tons of notes in a short time.Then I play the beginning of Chopin Nocturne Op 27 no 2. This is to test the beauty and resonance of the treble, to see how the piano can sing a melodic line.Then I play some of the Berg Sonata. The sharp dissonances in that piece really tell me a lot about the clarity of sound a piano has.Then I play some Bach or Mozart to see if the piano can sound light and not tubby.That is all.
I like going in with several categories to test.ToneVoicingProjectionevenness of note executionevenness of down stroke of one keyweight of actionevenness of action weight across keyboardrepetitionminimum key height for next repetitionfeel of the actionability to sing a melody on topability to sing a melody in the middlequality of bass in harmonic structurelength of note bodybi chord / tri chord breakclarity and fullness of lowest bass notesbriliance of top most notesnon harsh and fullness of sound when playing loudnuance and subtlety when playing softability to change tone color and not just volumecolor the una corda pedal contributesvarious degrees of una corda applicationfluidity in una corda shift mechanisimability to apply nuance with sustain pedalhow well fractional pedaling workseveness of sostenuto letoff tactile surface of keys (does it get slippery with sweat)width of black keys (I like them fat)sound with lid fully up and music rack downease of access to strings for 20th century plucking techniquessoft close fallboard?does music rack have multiple angles available?