Each planet neighbourhood can be a map sector; if they are too complex they can be split into a few parts (Solar system example: assuming extensive colonization making Moon interesting, treat Earth and Moon as two adjacent sectors rather than one).
I can't use it for my project (no sectors, just planets with starlanes) but I can't resist pursuing this concept I always loved sectors.
With a setup of planets and "starlanes" you simply don't have many void map sectors because nobody goes too far from planets; void sectors might be present in strategically important locations within a star system (e.g. the Solar System could have sectors for each planet, important satellites and asteroids, the sun and two empty ones "above" and "below" the orbital planes).
No, not squares. Sector shapes are irrelevant and effectively nonexistent, sector sizes are vague and easily fudged, and particularly with arbitrary long-range links, the graph structure of sector adjacency is going to be arbitrary and likely not planar.
To rephrase what you wrote. The map is divided into squares, each consisting of several planets/systems/asteroid belts/satelites/orbital basaes/etc. Fleets are placed in a sector, then they take a position on one spacial body they occupy. There are no disctances within a sector, all fleets can engange any unit within system.
The problem I see is stopping enemies. Like, if you move a fleet to a sector (just moe them into space, no planet targetted), then enemy targets your fleet, but you gave an order to move to the next sector, so at the end of turn the enemy has invalid target (you are not there anymore) and you moved to another sector, effectivelly passing through the enemy lines.
Actually, I suggested that a fleet can only exit a sector if nobody attacks them; I'm afraid I didn't make the assumption of simultaneous turns (orders for each fleet, battles of fleets attacking each other or converging to a location, planetary assaults, and finally splitting and coalescing surviving fleets) sufficiently clear.
If your fleet wants to stop an enemy fleet and they are in the same sector, just attack them every turn and they won't go anywhere, except perhaps taking the battle to planets or stations of that sector they want to conquer or hold.