If you want a true 120Hz gaming experience you need a monitor. TVs reproduce frames to mimic a 120hz refresh rate, they are still only capable of a 60hz input from a computer.
What would you suggest then? I was looking at ASUS and Benq monitors. Only issue that I would have with a monitor is my girl likes to play some of my games with me ie. Lego Marvel. and watch me play games like Alan wake