(This may be something that everyone in the entire world already knows, but I tend to be a little slow in that category) There is indeed a way to figure out when the princess will come. If you open the little pause tab at the bottom left corner of the screen a little menu will pop out. Click on "status". There you can find out how many customers you've had, how much "Gotchi" you have earned, and what your reputation is. Now your reptation is based on how many smiley face thingys you have won(obviously). To get the princess to come to upgrade your shop when you have a putchi shop, A.K.A. the first level, you must obtain 15 smileys. Then the princess will come. But if you were running the Burger Shop for instance, she would appear at the back of the line once you have gotton 15 smiley. She will obviously not fall from the sky and land at the front of the line. She waits like a normal Tama, for her turn. Anywho, to upgrade from Metchi (2nd level) to gotchi (3rd level) you must get 45 smileys, and from Gotchi (3rd level) to Royal (final upgrade) you must get 90. In other words,
First get 15, then get 45, then get 90.
I hope I have helped! (And am not making a fool out of myself by stating the obvious)