A puppet city is a lot more likely to build a monument and temple than it is to build a university and public school. With 10% more gold from temples this just increases their value by that much more. A newly founded city can produce 4 culture per turn in about 10-15 turns after it's founded, then up to 11 once a temple (20 or so turns) is up (and +25% more with Sistine Chapel). .
FROM MY EXPERIENCE
1 - Monument - Yes
2 - Temple - No
3 - University - Yes
Public school - Yes
Maybe it depnds on what type of victory we are playing for? I was playing for a cultural victory!