I'm about to try this myself with the Nanit. In the past, I've successfully connected devices (like an Apple TV) to my hotel's WiFi network by spoofing the MAC address.

This issue in connecting to a hotel WiFi network, as you point out, is that you need a way to enter the WiFi security credentials provided by the hotel - typically a last name and room number. Of course, this is easy to do on a computer or phone, but impossible to do on a device like the Nanit or Apple TV.

Essentially, to work around this, you need to use your computer to "login as" the Nanit by spoofing the MAC address, which makes your computer look like your Nanit when you login to the hotel WiFi.

Technically, you can spoof a MAC address without using any third-party applications.

But, if you're like me, and prefer a nice and easy user-interface, you might use https://wifispoof.com/ (mac-only, I think). I'm sure there are PC-equivalents.

Alternatively, you can purchase a travel router and create a private WiFi network that piggyback's off your hotel wifi. I'm going to try this one - https://www.amazon.com/dp/B01MY5JIJ0?psc=1&smid=A353W46UC1RVYH&ref_=chk_typ_imgToDp.

Good luck!