I want to get a Chromecast with Google TV.
Let's say that I'm sitting on the sofa in my apartment & I'm about to log onto my bank website on my laptop onto my 55" TV. I decide that I want to cast the bank homepage onto my TV.
Since casting is wireless, can anyone within the range of the wifi signal from my router see me log onto my bank website?
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I am not sure, but this kind of connectivity is as safe as your Access Point connectivity is safe. Also I think everybody who is in range can join your session as a guest at least.
Anyway I would not cast my session with my bank to TV...
Assuming your Wi-Fi is secured with WPA2, preferably AES, no one outside would be able to intercept that transmission.
If you have a nefarious flatmate who knows the password and who knows how to use technical tools such as Wireshark and is monitoring transmissions at the time, they could intercept.