It is easy to connect the Inverter with the proper sized 12VDC cable to the batteries. Then you can run as much as probably 100 feet of 120VAC Extension cord to where your home entertainment items are located without issues... I am not much of fan of the wall mounted 12VDC Power receptacles. They always got hot on me with the poor connections they offer when drawing over 5 AMPS or so....
I used WIREMODE wire maintenance kits from LOWES to hide my extension cords and only the multiport receptacle is visibly on the back of the tabletop around the home entertainment units.
I also would use a PURE SINE WAVE Inverter for any electronic units... It only takes one that doesn't like MSW TYPE inverter sine wave to ruin your day when it goes up in blue smoke.. Use to be the PSW Inverters were really expensive but not so these days. My 600WATT PSW AIMS Inverter only cost $149 and I never have to worry about anything going up in blue smoke.
I started out with a 150WATT unit and liked it so well went to a 300WATT unit to run more items - I finally ended up with the 600WATT PSW unit and have two locations in my setup that has emergency power being the Home Entertainment Area and the Bedroom night table area. I leave my items plugged into the 600WATT Inverter unit all the time even when I am connected to shore power at the camp ground. Always ON... My normal capacity used from the 600WATT PSW Inverter is around 300WATTS... Having some reserve power is important to us as we camp alot off the power grid and usually re-charge our 255AH battery bank everyday at 8AM each morning so using more power is not much of an issue with us.
Works good for us...
Roy Ken