"So I decided to see for myself," [Twoflower] was saying. "Eight years' saving up, this has cost me. But worth every half-rhinu. I mean, here I am. In Ankh-Morpork. Famed in song and story, I mean. In the streets that have known the tread of Heric Whiteblade, Hrun the Barbarian, and Bravd the Hublander, and the Weasel… It's all just like I imagined, you know." (1.6.3)
How important is exploration to the novel? It's basically the entire reason the novel takes place. Without the urge to explore, Twoflower would never have gotten on the boat. If he didn't get on the boat, he wouldn't have meet Rincewind. If he hadn't met Rincewind, well, you get the idea.
In the long afternoon they toured the city of Turnwise of the river. Twoflower led the way, with the strange picture box slung on a strap around his neck. Rincewind trailed behind, whimpering at intervals and checking to see that his head was still there. (1.12.1)
Rincewind acts as Twoflower's tour guide to Ankh-Morpork. At the same time, he becomes our guide to exploring Ankh-Morpork. Funny how that works, isn't it?
Rincewind stared muzzily at the recumbent tourist. At two recumbent tourists. (1.27.15)
Welcome to the party, Rincewind. He has now joined Twoflower and the readers as tourist of the Disc, though he has absolutely no desire to explore anything beyond a comfy room lacking in particularly sharp objects.
Picturesque meant—[Rincewind] decided after careful observation of the scenery that inspired Twoflower to use the word—that the landscape was horribly precipitous. Quaint, when used to describe the occasional village through which they passed, meant fever-ridden and tumbledown. (2.1.2)
It's all about location, location, location. No, wait—maybe that's perception, perception, perception. Let's try this: The joy of exploration results from your perception of the location rather than the location itself. Ah, there we go.
"How do you know there's treasure in there?" [Rincewind] said.
Hrun heaved, and managed to hook his fingers under the stone. "You find chockapples under a chockapple tree," he said. "You find treasure under altars. Logic." (2.10.107-108)
One of the reasons the characters explore is because they wish to find something, somewhere, whether that's a home away from home or altars hidden away in the derelict temples of demonic nether-beasts.
At its base [Wyrmberg] was a mere score of yards across. Then it rose through clinging cloud, curving gracefully outward like an upturned trumpet until it was truncated by a plateau fully a quarter of a mile across. There was a tiny forest up there, its greenery cascading over the lip. (3.1.2)
One of the joys of exploring literature, especially in the fantasy and science fiction genres, is that you'll never know what you'll find. Upside-down mountains? Why not?
The precise origins of the Mage Wars have been lost in the fogs of Time, but Disc philosophers agree that the First Men, shortly after their creation, understandably lost their temper. And great and pyrotechnic were the battles that followed—[…]. (3.3.3)
We also explore the history of worlds that have never existed, and you never know what you'll find there. At least, we assume these worlds have never existed, but you never know.
"But I've thought about dragons all my life!"
In this place the frontier between thought and reality is probably a little confused. All I know is that once I was not, and then you thought me, and then I was. Therefore, of course, I am yours to command. (3.13.24-25)
As Twoflower explores, he finds his dreams. While we highly recommend exploring the world until you find your dreams, we also recommend scratching real dragons off that bucket list unless you find an avenue into another dimension.
There was a sudden darkness.
There was a brilliant flash.
The sudden departure of several quintillion atoms from a universe that they had no right to be in anyway caused a wild imbalance in the harmony of the Sum Totality which it tried frantically to retrieve, wiping out a number of subrealities in the process. (3.18.15-17)
Thanks to a hiccup in the physics of the universe, Twoflower and Rincewind explore an entirely new dimension where people fly in the bellies of metal dragons and are fed honey-roasted peanuts until they are spit out at their destination. Physics really does allow us to explore some pretty crazy stuff, and fiction-tweaked physics doubly so.
"Sometimes I think a man could wander across the Disc all his life and not see everything there is to see," said Twoflower. "And now it seems there are lots of other worlds as well. When I think I might die without seeing a hundredth of all there is to see it makes me feel," he paused, then added, "well, humble, I suppose. And very angry, of course." (4.8.11)
The urge to explore for the sake of exploration seems to be at the core of Twoflower's character. He can never be satisfied unless he's exploring—it's one of those journey-not-the-destinations type scenarios.