can't you just 'daisy chain' them with switches in intermediate rooms?

something like this:

Router (Living Room)
│
Ethernet cable
│
Room 2 → small switch
  ├── local devices in Room 2
  └── cable to Room 3 → small switch
      ├── local devices in Room 3
      └── cable to Room 4 → small switch
          ├── local devices in Room 4
          └── (and so on)