My argument would be that:
One generation passes away, and another generation comes;
But the earth abides forever. - Ecclesiastes 1:4 New King James Version
Is clearly talking about the people of the earth when it uses the phrase "the earth".
A generation passes away, a Generation comes but the people abide forever, is obviously the meaning.
So gods people will exist forever, but the planet will eventually be destroyed. So where will they live? Well, when the time comes we can look to the bible for a historical precedent of what will happen. Clearly, just as in the days of Noah, god will instruct his people to build some kind of space Ark. This will also be a good opportunity for god to have another cull of people he doesn't like. And animals he doesn't like, and plants...
And just like another bible story he will lead his chosen people, in their space ark, to a new land, a land flowing with (alien) milk and (alien) honey, where they can butcher the inhabitants and take possession and live happily until that planets sun also goes nova and they move on again and again...
This doesn't answer what happens at the eventual heat death of the universe, but I'm tired now and am going to stop. :)