How big was the old TV?
Are you wanting to put the new TV in the same spot and cover up the hole?
LED 120V TVs are low current draws. a 40" Samsung is 46W normal operation, 117W max, 0.3W standby.
A nice Sony Blu-Ray player is 28W.
You are not going to watch a TV enough to drain your battery bank.
However, you have to be sure you can completely turn off the power at the plug - either a plug bar or a switched outlet. Today's modern electronics are bad about parasitic power drains.
You are also going to want to turn off features like WiFi, smart updating, etc. Those also drain power.
Running a 12V TV won't be any less power usage for your battery bank than a 120V TV except for the inverter overhead for the same size screen.
If you have a laptop with a Blu-Ray player/ drive and an HDMI port - it might be less power draw - but more hassle to hook-up/ unhook.
Personally, my old eyes can't really see any detail on a 19" TV from more than five feet distance. And the 12V TVs I've seen are very dim compared to a near identical 120V TV. Might be manufacturer differences, but too dim for me to use.
Now, if you were going with 80% boondocking without hookups - I'd suggest a lot more detailed math. But for occasional usage for 3-4 nights without power - the TV will be very low on your electrical worries.
EDIT - forgot to mention - as per the previous post - you MUST get a Pure Sine Wave inverter for the TV/Blu-Ray. Very likely the one supplied by your coach manufacturer is not PSW.