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:
\pagebreak, which has an optional argument with an integer between 1 and 4:
\pagebreak. 1 inserts a
\@lowpenalty, 2 a
\@medpenalty, 3 a
\@highpenalty and 4 is mostly equal to
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
\penalty-100 between two paragraphs you are indicating that breaking the page there is favoured.
Plain TeX (and I believe LaTeX too) has macros to hint where breaks should occur with increasing likelyhood:
\bigbreak. They insert penalties of
-200 together with
\bigskip, respectively. Those vertical skips are added only when the break does not occur (despite being favoured).
Also worth mentioning is
\goodbreak which is
\par\penalty-500. In this case nothing happens if the hint to break is not taken.
\fillbreak=\vfil\penalty-200\vfilneg which hints to break with a strength of
-200 and fills the remaining space in the page (if any) with blanck space to avoid bad stretchings if the break indeed occurs there. In case the hint is ignored
\vfilneg cancels the
\vfil and nothing happens.
So you have many options, and I recommend reading Chapter 15 for much more information with better explanations.