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I recommend a few words:
divāvihāra -- for example the page-long description of that here which starts ...
an expression which ... I consider to correspond to the “day’s abiding”, divāvihāra, mentioned in MN 35 at MN I 229, 23, instead of intending a “heavenly abiding”.
It's used in many suttas to indicate what monks do (or at least, where or when or for what purpose they go somewhere) in the afternoon.
That footnote also mentions some activities like "the divine eye" -- which is mentioned in suttas sometimes, in the context of the Buddha seeing that someone somewhere might benefit from his help -- I'm not sure what the best example of that is, Ud 3.3 was the first I find ("Then, encompassing with his awareness the awareness of the monks staying on the bank...").
also, sukhavihāra (dwelling pleasantly)
suññatāvihāra -- e.g. from MN 121
‘Ānanda, these days I usually practice the meditation on emptiness.’
‘suññatāvihārenāhaṃ, ānanda, etarahi bahulaṃ viharāmī’ti.
Ditto in MN 151, which also calls that Mahāpurisavihāra ("the meditation of a great man.")
Eventually, in DN 16:
Now I am frail, Ananda, old, aged, far gone in years. This is my eightieth year, and my life is spent. Even as an old cart, Ananda, is held together with much difficulty, so the body of the Tathagata is kept going only with supports. It is, Ananda, only when the Tathagata, disregarding external objects, with the cessation of certain feelings, attains to and abides in the signless concentration of mind, [19] that his body is more comfortable.
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Meditation. Sometimes Buddha meditated just for the sake of it even after enlightenment.
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This answer might overlap with ChrisW's, but I just want to quote some examples from the suttas.
The first activity is "day's abiding", which seems to be sitting down and resting or relaxing.
From Udana 6.1:
I have heard that on one occasion the Blessed One was staying near Vesālī at the Gabled Hall in the Great Forest. Then, early in the morning, he adjusted his under robe and — carrying his bowl & robes — went into Vesālī for alms. Then, having gone for alms in Vesālī, after the meal, returning from his alms round, he addressed Ven. Ānanda, "Get a sitting cloth, Ānanda. We will go to the Pāvāla shrine for the day's abiding."
Responding, "As you say, lord," to the Blessed One, Ven. Ānanda followed along behind the Blessed One, carrying the sitting cloth. Then the Blessed One went to the Pāvāla shrine and, on arrival, sat down on the seat laid out.
Seated, the Blessed One addressed Ven. Ānanda, "Vesālī is refreshing, Ānanda. Refreshing, too, are the Udena shrine, the Gotamaka shrine, the Sattamba shrine, the ManySon shrine, the Sāranda shrine, the Pāvāla shrine.
The second activity is simply meditation, specifically, absorption meditation in one of the jhana states. This is also called "imperturbable concentration".
From Udana 3.3:
Now, at that time the Blessed One was sitting in imperturbable concentration [either in the fourth jhāna, the dimension of the infinitude of space, or the dimension of the infinitude of consciousness]. The thought occurred to the monks, "Now, in which mental dwelling is the Blessed One now residing?" Then they realized, "He is residing in the imperturbable dwelling." So they all sat in imperturbable concentration.
Then Ven. Ānanda — when the night was far advanced, at the end of the first watch — got up from his seat, arranged his robe over one shoulder, stood facing the Blessed One, paying homage with his hands placed palm-to-palm over his heart, and said to him, "The night, lord, is far advanced. The first watch has ended. The visiting monks have been sitting here a long time. May the Blessed One greet them." When this was said, the Blessed One remained silent.
Then a second time, when the night was far advanced, at the end of the middle watch, Ven. Ānanda got up from his seat, arranged his robe over one shoulder, stood facing the Blessed One, paying homage to him with his hands placed palm-to-palm over his heart, and said to him, "The night, lord, is far advanced. The middle watch has ended. The visiting monks have been sitting here a long time. May the Blessed One greet them." When this was said, the Blessed One remained silent.
Then a third time, when the night was far advanced, at the end of the last watch, as dawn was approaching and the face of the night was beaming, Ven. Ānanda got up from his seat, arranged his robe over one shoulder, stood facing the Blessed One, paying homage to him with his hands placed palm-to-palm over his heart, and said to him, "The night, lord, is far advanced. The last watch has ended. Dawn is approaching and the face of the night is beaming. The visiting monks have been sitting here a long time. May the Blessed One greet them."
Then the Blessed One, emerging from his imperturbable concentration, said to Ven. Ānanda, "Ānanda, if you had known, not even that much would have occurred to you (to say). I, along with all 500 of these monks, have been sitting in imperturbable concentration."