As well as checking local networks, I would also recommend getting a cheap bug detector (RF transmission and IR lens detector type) such as a CC308+ or similar model - they are cheap (price point around ~$20 USD) and while not terribly precise have the benefit of a huge detection range (1mz to 6.5ghz, which is easily enough to pick up WiFi devices and other common transmitter frequencies). The IR LEDs and aperture also make it easy to spot hidden cameras - they show a noticeable glint under the LED strobe, even when concealed.<p>Commenter jonnismash mentioned that nmapping the network might be illegal in some jurisdictions, this has the benefit of avoiding that risk.
Which would obviously not work if the rental is using VLAN/Guest network feature to isolate the main network.<p>Most decent consumer routers do this.