Plan on running your generator about 4 hours each morning (at least) if your batteries have been used much during the evening/night, It takes a long time time to recharge even partially discharged batteries. In fact, when I move from RV park to RV park, It takes about 3 days for the remote indicator on my Progressive 9260 Converter/Charger to indicate that the battery system is fully charged again.
If you DO get an inverter, plan on using it for SHORT (less than 5 minutes) uses on high-current stuff like microwaves or toasters. The 12 volt amp draw from your batteries for something like that can be 100-150 amps continuously. Also, I would recommend a "Pure Sine Wave" inverter that is more expensive and less efficient (more waste power) than the "modified sine wave" types. A lot of modern electronics in microwaves, computers, TV's don't like modified sine wave power.
BTW, I am changing my mind about boondocking and solar power and have a 240 watt, 5 foot by 3 foot, residential solar panel that I have not yet installed, a controller for it, and installed wiring that I can probably pull out pretty easily, if you are interested. Although we are both Californians, most likely we are 500 miles apart. You (or anyone) can PM me if you are interested. I am planning right now to be near Bakersfield for the month of February, if that helps. I could bring the panel along.