Having built your space elevator, you're now in a position to colonize other worlds. The obvious first destination is Mars. You get there in a cloud of small, mass-produced ships, and once you've got there one of the first things you do is drop down a cable and build a Martian space elevator. You're up in orbit anyway, so why not take advantage of the fact? Again, this is the metaphorical aspect of the space elevator: as soon as just one exists, it opens up a vast range of new possibilities. However, you'll probably need to land a team by some other method in order to construct the complex at the bottom to which the cable will be tethered.
Mars isn't a great place to live, so the next step is to terraform it, to make it more earthlike. There are reasonably plausible methods for doing that, detailed at length in Kirn Stanley Robinson's series Red Mars, Green Mars, Blue Mars. Mars is no improvement when it comes to meteor-strikes, but at least the colony on Mars is unlikely to get wiped out at the same time as the main population on Earth. Because life is reproductive, if one of them does get wiped out, it can quickly be re-colonized from the other. After a few centuries, you'd hardly notice any difference. Still, it may be better to be more ambitious and go to the stars. By the time we're ready for that, we'll have interferometer telescopes good enough to spot which stars have suitable planets. The only problem, then, will be to get there.
There are plenty of suggestions, and we won't add to them. Think of mid-Victorians predicting life in the 1990s. The dynamic of extelligence is emergent or, to put it another way, we haven't the faintest idea what we'll think of next but it'll probably surprise us.
One way, if all else fails, is the Generation Ship, a huge vessel that can hold an entire city of people, who live, breed, educate, and die throughout the centuries-long journey. Make it big and interesting enough, and they may even lose interest in the destination. The Discworld almost counts as one of these; it's on a journey, the inhabitants don't know where they're going, the designers have given it a small controllable sun (thus doing away with all those nasty fluctuations) and no less than five bio-engineered creatures positively delight in clearing local space of intrusive debris ...
Back on our world, you could take a really long-term view and seed the galaxy with genetically engineered bacteria, carefully tailored so that whenever they find a suitable planet they eventually evolve into humanoid life (or life, at least). We would die out, but maybe our fleet of cheap, slow ships might seed a few new Earths somewhere.
There's no shortage of ideas. Some might even be practical. The galaxy beckons. We might die trying, but since we're going to die anyway, why not try?
And what will we find out there? Will we find a radically different kind of 'space elevator', for instance? Well, if there are aliens that live on neutron stars, as Robert L. Forward describes in Dragon's Egg, then they might escape by tilting their world's magnetic axis, turning it into a pulsar, and surfing its plasma jet. Perhaps all those pulsars were formed in this way. Like any 'space elevator', if you can manage the trick once, the rest is easy. The inhabitants of one neutron star managed it, and colonized all the others, founding the Pulsar Empire ...
And since we can envisage new kinds of physical space elevator, there must surely also be new kinds of metaphorical space elevator. Not just aliens a bit like us, but radically different new kinds of life.
What else could live on a neutron star?
They're waiting.
YOU NEED CHELONIUM
'THAT,' SAID THE DEAN, 'was a very unpleasant business. Good thing we weren't really there.'
Rincewind was sitting at the end of the long table, his chin on his hand.
'Really?' he said. 'You thought that was bad? Try having a comet land on you. That really makes your day.'
'It was the music that really got on my nerves,' said the Senior Wrangler.
'Oh, well, good job the planet's a snowball, then,' said Rincewind.
'I call this meeting to order,' said Ridcully, thumping the table. 'Where's the Bursar?'
The wizards looked around the main hall of the High Energy Magic building.
'I saw him half an hour ago,' the Dean volunteered.
'We are quorate, nevertheless,' said Ridcully. 'Now ... the magic flux is almost run down, although HEX reports that the model universe appears to be continuing on internal power. Amazing the way the whole place seems to strive to keep existing. However ... gentlemen, the project is at an end. All it is has taught us is that you can't make a world out of bits and pieces. You need chelonium for a proper world. And you certainly need narrativium, otherwise the life you get is a lot of opening chapters. A comet is no way to end a story. Ice and fire ... that's very primitive.'
'Poor old crabs,' said the Senior Wrangler.
'Goodbye, lizards,' said the Dean.
'Farewell, my limpet,' said the Lecturer in Recent Runes.
'What were the ones that left?' said Ponder.
'Er ...' said Rincewind.
'Yes?' said the Archchancellor.
'Oh, nothing. I had a thought... but it couldn't possibly work.'
'Some of the bears seemed quite bright,' said Ridcully, who had naturally sided with a lifeform that resembled him in several particulars.
'Yes, yes, it was probably the bears,' said Rincewind quickly.
'We couldn't watch the whole world ail the time,' said Ponder. 'Something could have evolved quickly, I suppose.'
'Yes, that's right, something probably evolved quickly,' said Rincewind. 'I shouldn't think there was any unauthorized interference in any way.'
'Good luck to them, whatever shape they're in,' said Ridcully. He assembled his papers. 'That's it, then. I won't say it hasn't been an interesting few days, but reality calls. Yes, Rincewind?'
'What are we going to do with the snow globe, I mean, the world?' said Rincewind.
As one wizard, they looked across at the world spinning gently in its dome.
'Is it any use to us, Mister Stibbons?' said Ridcully.
'As a curiosity, sir.'
'This university is stuffed with curiosities, young man.'
'Well, then ... only as very large paperweight.'
'Ah. Rincewind ... you an the Professor of Cruel and Usual Geography, so I suppose this is right up your street...'
There was a rattle from HEX's tray. Ponder pulled out the paper.
It said: +++ The Project Must Be Kept Safe +++
'Fine. Rincewind can put it on a high shelf so that it doesn't get knocked,' said Ridcully, rubbing his hands together.
+++ Recursion Is Occurring +++
Ridcully blinked at the writing.
'Is that a problem?'
HEX creaked. There was a flurry of activity in the ant tubes. Eventually the write-out clattered for some time.
Ponder picked up the message.
'Er ... it's addressed to Mrs Whitlow,' he said. Er ... it's rather odd...'
Ridcully looked over his shoulder.
'"Don't Dust It",' he read.
'She's a devil with a duster,' said the Senior Wrangler. 'The Dean nails his door shut when he leaves his study.'
The write-out clattered again.
'"This Is Important",' Ponder read.
'Not a problem, not a problem,' said Ridcully. 'So on to the next item. Ah, yes. We have to shut down the reacting engine. No, don't get up, Rincewind, I've had the door locked. The interior of the squash court is still just a tiny bit not entirely completely safe, is that right, Mr Stibbons?'
'Very definitely!'
'And therefore the area within it quite clearly counts as...'