Resupply ships are fun, and make awesome infinite range scouts, pirate hunters, and 'proactive' salvagers.
If you fit them with construction bays you can use them to repair ships you capture in-situ, even each other if you deploy them in pairs (if you haven't slogged down the damage control tree yet).
You can put LRS on freighters to pretty much blanket your empire in sensor coverage at zero cost to you (besides your cargo ships having about half the effective range you'd expect).
Constructors are another decent place to put them, but not my preference as I prefer speed, endurance and wing of fighters. Honestly, fighter bays are probably the single most useful component you can add to constructors.
LRS on 'normal' state ships are at best a stopgap until you can get something more suitable, as they are either confined to systems where they're vulnerable or they're constantly returning to refuel and thus not being where you need them.
Ports are always a good place for LRS, along with mining stations for complete coverage (again, abuse of the huge private treasury).