Brian - They sell a great 600W PSW AIMS 12VDC Power Inverter. That is what we have here for all of our low wattage things like the TV etc... I have the 20inch VIZIO HDTV in my camper and use a BATWING antenna on top...
When we are camping running a few of the 120V items off of it is usually only around 300WATTs being consumed...
We have our camping day/night all planed to reduce my battery bank to its 50% charge state around 8AM the next morning. Then I will run the generator during that time to recharge my batteries back up to their 90% charge state which takes around three hours of generator run time... We usually are camping in the Natl Forest somewhere that allows the generator use from 8AM to 8PM. I image your Natl Forest areas do the same thing. They all use to be 8-10AM and then again 4PM to 7PM. ALot now allows them 8AM to 8PM and never after 8PM... Gotta have a Power Inverter for those times...
AMAZON has the 600WATT PSW for around $150...
Roy Ken