Regular 120V electrical outlets will not work unless plugged into "a regular 120V hookup" or a generator.
If you want regular 120V power without either of those, you need an inverter. This is a separate device that converts the 12V DC power from your battery into "regular" 120V AC power.
However, there is no free lunch. Inverters are quiet and convenient, but they require a LOT of battery power, depending on what you power with the inverter. A small TV, no big deal, but a hair dryer, toaster, microwave... That's big time battery drainage that has to be recharged by a large solar array on the roof, many hours of driving (to let the alternator recharge the batteries), several hours of running the generator (to let the onboard battery charger do its work), or plugging into 120V power for several hours.
The battery bank and solar array can be a large investment, and requires knowledge to use and maintain properly. If you're willing to spend the time to become an electrical geek and the money for the system, it may be worth looking into.
With the other alternatives, you may as well just use the generator or shore power directly in the first place. Run the generator just long enough to dry your hair or microwave your popcorn, only a few minutes vs. several hours.
For the average camper, really the best thing to do is try to find 12V DC, or propane-powered alternatives to 120V AC appliances. Or, run them with a generator.