Buddha's advice for after enlightenment
There needs to be some caution/qualifications when discussing arahants just as there should be when discussing the Buddha. SN 44.1 discusses this caution and it applies to arahants as well.


  "so too, great king, that form by which one describing the Tathagata might describe him has been abandoned by the Tathagata, cut off at the root, made like a palm stump, obliterated so that it is no more subject to future arising. The tathagata is liberated from reckoning in terms of form; he is deep, immeasurable, hard to fathom like the great ocean."


In SN 35.135:


  I do not say of those bhikkhus who are arahants . . . that they still have work to do with diligence in regard to the six bases for contact. Why is that? They have done their work with diligence; they are incapable of being negligent.


There is one other teaching that I know of regarding what arahants do but I can't find it right now. In it the Buddha says that arahants continue to dwell with the 4 mindfulness established. Maybe someone else can find that reference?