When overnighting in a temporary location, like a Walmart, running a generator after dark is "frowned upon".
Admittedly, if you are parked off to the side your 2000W inverter generator is probably quieter than a semi idling, so where you park is an issue. Also, using a portable generator in a parking lot is a very tempting item for a thief. Make sure it is locked up well. Late night TV can be done with a single battery and a 300W inverter.
I would go with a either a Predator or Champion 2000W inverter and get a Micro-Easy Start for next year or plan on buying a second generator.