What you decide to do depends on what you like about the game.
Once you complete all the puzzles, there aren't any more 'official goals' left in the game. There are still many more island events that you haven't seen, which will change the circumstances in the game - and they present some interesting choices to make. There are also a lot of villager behaviors that you may not have seen unless you've spent a fair amount of time 'peep watching.'
On the other hand, the village can get pretty crowded in the later stages of the game, and many people start over to try some new strategies, or play the game on a different setting. I've played dozens of different games and chased some fun challenges that I set for myself - like solving puzzles as early as possible in the game, or finishing all of the puzzles (except the graveyard) without any of my villagers dying. There are many interesting things to do with the game!