You can get a 300 - 500 watt inverter for about $30 - $50, and plug it into a cigarette lighter receptacle.
You can install a cigarette lighter receptacle near the TV set, or near your dinette table, or your bedroom nightstand, or all three. I ran #10 wire back and forth from the battery in one RV and from the fuse panel to the receptacle in another RV. What ever is closer, or easy to do. Put in a 30 amp fuse, and you are done.
As for batteries, a pair of batteries will hold about 2,000 watts. This is plenty for most RV's. Your RV will use 35 amp hours per day just to run the refrigerator, CO meter, and propane detector. A average group 27 battery is 105 amp hours. Group 24 is about 85 amp hours. Golf cart batteries are 220 amp hours, but it takes two of them to make up 220 amp hours at 12 volts.
Your TV set probably uses between 85 and 110 watts, or about 8-10 amp hours per hour. Cell chargers are much more efficient, with a plug in 120 volt one using about 0.5 amp hours per hour, while direct 12 volt one might be as little as 0.2 amps per hour.
DVD player is about 20 watts, or about 1.5 amp hours per hour. It might be more efficient to use a computer, about 1.5 amp hours including the screen.
Have fun boondocking! I always loved to find a forest service area, or campground over the private campgrounds that seem to be so crowded.
Fred.