On the day you think a villager will put their house down, you have to create a new character (do NOT use your mayor). If the plot is where you want it to be, then create a house for that character so that you can save after Isabelle has given you the resident card, and then you can delete that character. If the plot is not where you want it to be, you can quit without saving and repeat the process until you like where they've plotted.
If the villager's been bought or given away by another person, normally the plot will be there next day; if you've adopted them through the campsite, it will normally take 2 days. However, I suggest you create characters every day so as to avoid surprises.