Shortest distance/path between two households
This problem is well considered and learned in recent decades as every GPS device faces this problem.

In practice (AFAIK), the standard way of facing this problem is by the usage of distance oracles, which usually (or more correctly, used to) approximate the distance between every two nodes by keeping only a $k\times n$ distances tables for a well-selected $k$ vertices.

The lastest result I'm aware of, keep a data structure of size $O(kn^{1+1/k})$, answering queries in $O(1)$ time and giving a stretch (i.e. the return value $\delta$ is promised to suffice $d\leq \delta \leq d\cdot s$). of $2k-1$.

Alternatively, if you're looking for a stretch smaller than 2, I suggest looking at this paper.