So I have 10 villagers right now. One of them asked me to move out today and I said yes. I'm wondering when can I go island hopping to find a new villager to replace him before a random takes the spot?
you have to wait for the villager to move out. once they’re gone and their plot is unoccupied, that’s when you’ll be able to find villagers during island tours again
You get the full day after the villager has moved out (their plot is empty) to go island hopping and look for a new villager. I wouldn't take more than a day because then you'd risk getting a random move-in