When must an Instant be played that prevents damage?
Yep, in order to prevent a creature from dying in combat, the spell needs to be cast before combat damage is dealt. And the last opportunity to cast spells before combat damage is dealt is during the declare blockers step, just after blockers are actually declared.

There is one exception: if any creatures with first strike or double strike are involved in combat, there will be a combat damage step to handle their damage, prior to the time when other non-first strike combat damage is dealt. As part of that combat damage step, you get a chance to play spells and abilities, which could include the Harm's Way. So you could get away with playing it later than the declare blockers step if there is a first striking or double striking creature in combat, as long as it's not the one you want to prevent the damage from.

To make everything explicit, here's an outline of the combat phase:


Beginning of combat step

Play spells and abilities

Declare attackers step

Actually declare which creatures are attacking
Play spells and abilities

Declare blockers step

Actually declare which creatures are blocking and how
Play spells and abilities

First strike combat damage step, only if creatures with first (or double) strike are involved in combat

First strike combat damage is assigned and dealt
Play spells and abilities

Combat damage step

Non-first strike combat damage is assigned and deal
Play spells and abilities