Background music, cocktail piano - whatever you want to call it - is a venue I have never pursued. When the opportunity came (as it often does, when I wasn't looking for it), I mentally shrugged - and pulled together repertoire. The gig: 2 hours a day, once or twice a week, play background music in an office building lobby, surrounded by modern art, orchids and random businessmen. Selecting music to fill two hours (avoiding any repeat pieces) took some thought, but I was amused to find collaborative repertoire I've performed in other venues translates just fine when played solo. For example, popular opera arias (O Mio Babbino, Quando Men Vo, Summertime), showtunes (selections of Bernstein, Sondheim, Cole Porter) and wedding music (Canon in D, Jesu Joy of Man's etc, Schubert or Bach/Gounod Ave Maria) all work well even without a singer/instrumentalist.
Solo piano music selections usually are 'whatever pieces you know how to play', but also consider that people enjoy familiar pieces. Classical chestnuts people recognize, such as Clair de Lune, Moonlight Sonata and Gymnopédie No 1, are all appreciated and not too difficult to work up. I add some contemporary pop music in as well - but is isn't required. I find the gig a nice temporary departure from what I usually do, and enjoy the challenge of providing atmosphere while avoiding monotony. All pianists should have their own folder of at least 60 minutes of music - ready to go. It comes in handy on several occasions, such as wedding and funeral gigs, providing incidental music for church services and so on.
*Quick side note - I was sad to discover that Nordstrom has let their pianists go.