Quick Tip: Have a few pieces…
Have a few pieces in your bag. These should be pieces that can be played well with minimal practice time and sound good.
I keep a binder of “gig” music that’s all very easy, sounds good and is easy to get under my fingers (45+ minutes of music that can be brought back in a few hours of practicing).
In addition, when asked to play “anything!” you can have a few pieces memorized to whip out whenever. It eliminates that awkward, “Well…I’m working on some things right now…”
I agree completely, when you can smile and say oh yeah “here’s a nice piece” and then play without undue hesitation most people will enjoy it, more so than if you preface your performance with a self depreciationg preamble. These pieces should be well within your technical command simple and fairly short, for me that would be pieces like Lagrima, Adelita and some Carcassi Etudes. By them I’m warmed up and if there’s a desire to hear more demanding music I’m warmed up.