You could take the train to Forest Hill from where it is only a short walk to the Horniman Museum and gardens.

Seriously though, with trains every few minutes, we should start to use the train between our stations more often. Next year, rather than getting an annual ticket from FH to London terminals, I might get it from Crystal Palace so that I can pop down to CP or Sydenham whenever I want. For the moment I shall have to make do with HOP, NXG, and 'Artley' (listen to ELL on train announcements to find out where Artley is located).