What is life like after having achieved nirvana?

The only answers you'll get to this are answers-by-analogy, because realization is experiential. I mean, if I asked you questions like:

• What's it like to throw a baseball?
• What's it like to eat lasagna?
• What's it like to sing?

I doubt you could give me any effective answers. I will say that the best analogy I know of comes from daoism, which suggests that mastery is like a pond after the mud settles. Everything is the same - the same pond, the same water, the same mud - but everything is different. After the mud settles, the water is clean, clear, and sweet.

Please see this answer for details.

The fully liberated ones (arahants) tend to live as monks or nuns, because they can no longer live the lay materialistic life. They are completely free from all mental suffering and mental defilements.

They may experience physical pain, but they can mentally endure it. Physical pain does not lead to mental suffering for them.

They no longer experience greed/ lust, aversion (including hate) and delusion. They no longer crave for sensual pleasures or crave to become something. They don't experience boredom.

They may plan to do something, but they never plan to become something or somebody. They don't brood about the past or, dream or worry about the future.

Where the unenlightened feel boredom due to inactivity or feel loneliness due to lack of company, the arahants feel completely at ease and peaceful, and even prefer this. Their mental state is peaceful, free of "noise" and mental agitation of any kind.

They eat or take care of their health only out of necessity for maintenance and not with desires for sensual pleasures or to become something or somebody.

Their mental state will be that of peace and bliss all the time.

From the Dhammapada:

90. The fever of passion exists not for him who has completed the journey, who is sorrowless and wholly set free, and has broken all ties.

91. The mindful ones exert themselves. They are not attached to any home; like swans that abandon the lake, they leave home after home behind.

92. Those who do not accumulate and are wise regarding food, whose object is the Void, the Unconditioned Freedom — their track cannot be traced, like that of birds in the air.

93. He whose cankers are destroyed and who is not attached to food, whose object is the Void, the Unconditioned Freedom — his path cannot be traced, like that of birds in the air.

94. Even the gods hold dear the wise one, whose senses are subdued like horses well trained by a charioteer, whose pride is destroyed and who is free from the cankers.

95. There is no more worldly existence for the wise one who, like the earth, resents nothing, who is firm as a high pillar and as pure as a deep pool free from mud.

96. Calm is his thought, calm his speech, and calm his deed, who, truly knowing, is wholly freed, perfectly tranquil and wise.

97. The man who is without blind faith, who knows the Uncreated, who has severed all links, destroyed all causes (for karma, good and evil), and thrown out all desires — he, truly, is the most excellent of men.

98. Inspiring, indeed, is that place where Arahants dwell, be it a village, a forest, a vale, or a hill.

99. Inspiring are the forests in which worldlings find no pleasure. There the passionless will rejoice, for they seek no sensual pleasures.

Arahantavagga of Dhammapada

The six-senses cease creating consciousness. The consciousness that usually arises out of these six-senses is very noisy, even when one seems settled and relaxed. In Buddhism, it is known as the samsaric consciousness, which is best illustrated visually in the Tibetan Wheel of Life and best described by the Buddha in Dependent Arising as a mass of suffering. This type of consciousness largely comprises an unsettling energy coupled with a tremendous desire to ease the discomfort it creates. What we understand to be comfort is actually the release from the activities that we assume to be a remedy: the acquisition of objects, people and situations only gives temporary relief, but it is only the relief from striving itself. This antagonizes the restlessness, and so humans go round and round in a crazy loop because the fundamental issue still remains.

Enlightenment is the understanding that one does not need to suffer in that way. The six-senses no longer fall under the illusion that captivates 99 percent of people on earth - that type of consciousness has ended, but if you were to touch the body, there still remains heat, one still speaks and moves around. But you might still knowingly fall into the innocence along with everyone else. After all, we are 2-year-olds farting about in a huge sandpit. Some of us do it nicely, some of us perhaps not so. That's OK, because it's all the same childlike innocence.

It doesn't mean you become perfect. You might still roll a ball of snot between your thumb and index finger and perhaps flick it into an obscure corner of the room (that reminds me, I must vacuum the floors this week). And who knows, you might even tell someone off.

Ānanda once asked the Buddha a similar question:

MN115:3.2: “Sir, how is a mendicant qualified to be called ‘astute, an inquirer’?”

The Buddha responds at length and touches most succinctly on the unconditioned:

MN115:9.3: There are these two elements:
MN115:9.4: the conditioned element and the unconditioned element.
MN115:9.5: When a mendicant knows and sees these two elements,
MN115:9.6: they’re qualified to be called ‘skilled in the elements’.”

So the short answer is to understand the unconditioned:

SN43.12:1.3: And what is the unconditioned?
SN43.12:1.4: The ending of greed, hate, and delusion.
SN43.12:1.5: This is called the unconditioned.

Furthermore...

AN3.47:2.1: “Unconditioned phenomena have these three characteristics.
AN3.47:2.2: What three?
AN3.47:2.3: No arising is evident, no vanishing is evident, and no change while persisting is evident.

Pragmatically, one might simply observe that the unconditioned life (i.e., a life lived in resonance with limitless love, compassion, rejoicing and equanimity) is a life lived free of the boundaries imposed by suffering.

SN41.7:6.2: Greed, hate, and delusion are makers of limits.
SN41.7:6.3: A mendicant who has ended the defilements has given these up, cut them off at the root, made them like a palm stump, and obliterated them, so they are unable to arise in the future.

The not very helpful but probably accurate response is Nirvana is ineffable

The more helpful answer would be to direct you a few books.

Daniel Ingram's book Mastering the Core Teachings of the Buddha, An Unusually Hardcore Dharma Book is a very detailed account of what the higher stages of realisation are like (to him) up to and including Nirvana from an arhant perspective. I think he has since modified this claim but it's all pretty high level stuff. It is freely available for download at the above link.

Also, there is Rob Burbea book Seeing that Frees. While Rob Burbea doesn't make any specific claims for his own level of realisation - it's clear that he is a very experienced insight meditator and he gives a clear account of what that is like plus instruction on how to get there. You'll have to pay for that book.

Probably the most helpful thing to say is just engage with Buddhist practice as much as you are able under a teacher that you trust. And do your best. I personally wouldn't read the above two books if I wasn't practicing, as there is just a whole heap of misunderstanding and grasping that can come from it - especially the Daniel Ingram one.

They are great books though, so everyone makes their own decision about how much they want to know about the stages of the path and at what point, and how to balance this with their own practice.