If you set up Apple TV 4K on one TV - is there any settings setup on Apple TV if you change it to another TV set?

Should work fine on both devices, I take my 4K Apple TV with me on vacation (normally AirB&B locations) and it plugs into any TV with HDMI input with no problems. The only setup I need to do is to join it to the network at the new location. I'm assuming both of your TV's would be on the same network. The only thing I can think of that may be an issue is network coverage where both TVs are located. If you get a strong network signal in both locations you should be good to go!