Because TWOK never really needed to explain what he would have done with Genesis (assuming he entirely understood it anyway - he initially stole it merely as bait to get Kirk's attention and draw him in, then used it as a last ditch bomb) it's very hard to imagine where his mind would have gone given he was driven by revenge for most of the film and never had the chance to have that and then be able to say 'What am I going to do tomorrow?'.
Would he have quietly slipped off in Reliant?
He seemed happy to have had the chance to build a world before, he may have been content to find another planet to try on. But of course he once had immense power and once he had mined the ship's database of information about the world he was now in (and cleansed himself of vestigal things like 2D thinking) he may have thought about a bigger power play.
But he would have had a very hard time doing that because on paper his biggest asset is his biggest problem. Because he can't actually use Genesis IMO.
He can't use it as a deterrent because he only has the one. And to deter people you need to know what could happen to you if you don't comply. But the Genesis project was top secret and then buried by the Federation - so your wider Earth or anywhere else populace should know nothing about it. So, he would have to demonstrate it's power.
Except he only has the one. So if he uses it no more deterrent - he could bluff of course but those in Starfleet who would know of Genesis would know only one existed. He could try and figure out how to make another one (or a dirty version of one) but we don't know if that would be feasable without the likely generous funding of The Federation.
So Genesis might not be the answer for him.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist