Buddha meditation under the bodhi tree

Our Bodhisatva / Buddha had very high levels of Samadhi hence he could have stayed many days without moving of doing anything else. Deep Samadhi brings down your metabolism so you can stay for long periods without food, water or air. There might have been times when he would have done it in one sitting and sometimes may had have gone for alms as per @ChrisW answer.

There's a line in the Ariyapariyesana Sutta which I think implies he "did normal things" as well as meditating:

Ariyapariyesana Sutta: The Noble Search

"In search of what might be skillful, seeking the unexcelled state of sublime peace, I wandered by stages in the Magadhan country and came to the military town of Uruvela. There I saw some delightful countryside, with an inspiring forest grove, a clear-flowing river with fine, delightful banks, and villages for alms-going on all sides. The thought occurred to me: 'How delightful is this countryside, with its inspiring forest grove, clear-flowing river with fine, delightful banks, and villages for alms-going on all sides. This is just right for the exertion of a clansman intent on exertion.' So I sat down right there, thinking, 'This is just right for exertion.'

"Then, monks, being subject myself to birth, seeing the drawbacks of birth, seeking the unborn, unexcelled rest from the yoke, Unbinding, I reached the unborn, unexcelled rest from the yoke: Unbinding. Being subject myself to aging... illness... death... sorrow... defilement, seeing the drawbacks of aging... illness... death... sorrow... defilement, seeking the aging-less, illness-less, deathless, sorrow-less, unexcelled rest from the yoke, Unbinding, I reached the aging-less, illness-less, deathless, sorrow-less, unexcelled rest from the yoke: Unbinding. Knowledge & vision arose in me: 'Unprovoked is my release. This is the last birth. There is now no further becoming.'

So, doesn't that imply meditation, but also alms-going etc.?

The Buddha was human and was by that time practicing the Middle Way: therefore, I think, no asceticism.

But there are other suttas which imply otherwise, for example:

Bodhi Sutta: Awakening

I have heard that on one occasion, the Blessed One was staying at Uruvelā on the bank of the Nerañjarā River at the root of the Bodhi tree — the tree of awakening — newly awakened. And on that occasion he sat at the root of the Bodhi tree for seven days in one session, sensitive to the bliss of release. Then, with the passing of seven days etc.

Bhikkhu Bodhi narrates it as follows:

The Buddha and His Dhamma

Now he was alone, and complete solitude allowed him to pursue his quest undisturbed. One day, when his physical strength had returned, he approached a lovely spot in Uruvela by the bank of the Nerañjara River. Here he prepared a seat of straw beneath an asvattha tree (later called the Bodhi Tree) and sat down cross-legged, making a firm resolution that he would never rise up from that seat until he had won his goal. As night descended he entered into deeper and deeper stages of meditation until his mind was perfectly calm and composed. Then, the records tell us, in the first watch of the night he directed his concentrated mind to the recollection of his previous lives. Gradually there unfolded before his inner vision his experiences in many past births, even during many cosmic aeons; in the middle watch of the night he developed the "divine eye" by which he could see beings passing away and taking rebirth in accordance with their karma, their deeds; and in the last watch of the night he penetrated the deepest truths of existence, the most basic laws of reality, and thereby removed from his mind the subtlest veils of ignorance. When dawn broke, the figure sitting beneath the tree was no longer a Bodhisatta, a seeker of enlightenment, but a Buddha, a Perfectly Enlightened One, one who had attained the Deathless in this very life itself.

For several weeks the newly awakened Buddha remained in the vicinity of the Bodhi Tree contemplating from different angles the Dhamma, the truth he had discovered. Then he came to a new crossroad in his spiritual career: Was he to teach, to try to share his realization with others, or should he instead remain quietly in the forest, enjoying the bliss of liberation alone?

In the above, the first paragraph describes meditation in which the Buddha resolved not to move at all, and reached enlightenment after one night. After he is enlightened, the next paragraph describes him remaining "in the vicinity of" (which means "near") the Bodhi Tree for several weeks.