I know the obvious move for the sequels is to show Han being a General and settling down with Leia, etc etc... but I think I'd much rather see him striking off on his own and becoming a bit of a renegade again. And maybe even having some of that grumpiness and edge that Ford himself now has.
He might have been willing to play along to take down the Empire, but I just can't imagine him wanting to be the noble, upstanding leader forever.
Leia also had an independent streak in her, and there is probably no place for a princess in the republic. I can certainly see a story where the two of them are living off the grid, but have some vitally important knowledge that requires the "new" heroes to seek them out.