How do I tell LaTeX, "if you need to put a page break, this is a good place to put it" ?
Since you are asking for a LaTeX solution:
Leslie Lamport explains all about it in the manual.
Look at Chapter 15 of the TeXbook for all the details, but basically you should add negative penalty where those breaks are desired.
For example, the TeXbook says that if you say
Plain TeX (and I believe LaTeX too) has macros to hint where breaks should occur with increasing likelyhood:
Also worth mentioning is
So you have many options, and I recommend reading Chapter 15 for much more information with better explanations.