A 32-inch VIZIO HDTV will draw around 85WATTS of power from 120VAC. This would be provided when you plug into camp ground shore power connections.
When camping off the power grid you could easily power this with a 300W PSW Inverter directly connected to your deep cycle battery. To insure you won't run down your battery most folks will always have two batteries installed for when camping off the power grid.
Like most of us you probably will want to add more 120VAC items to your Inverter when camping off the power grid. I ended up with consuming around 250WATTS of 120VAC Items we wanted to run each night when camping off the power grid. This is about a 20AMP power drain especially between 8PM and 11PM plus some of the other parasitic keep alive power drains which would drain our 255AH battery capacity system down to 12.0VDC by 8AM the next morning. We would have to re-charge our batteries back up to their 90% charge state in a three generator run time using smart-mode charging technology.
Alot of camp grounds have generator run time restrictions so if this is the way you want to go you have to be able to re-charge in as quick of time as you can which is a three hour generator run time.
We love camping off the power grid and do it alot. We had to do some planing to get to this point and we are very successful doing it now with the game plan being running all the 120VAC item we want to run from an Inverter and 12VDC items directly from the battery and be able to recharge the next day at 8AM so we can do it all over again for the next day/night run off the battery... For us this including using smart mode charging converter/charger unit, adding more batteries, changing out all of the automotive incandescent bulbs for LED low current lights, and doing things to conserve energy.
There is not many way you accomplish this and still be successful about it.
If you just show up it will most likely get dark on you around 10PM at night...
Roy Ken