No doubt adding solar is a good idea and can be done whenever you begin to camp for many days without shorepower. For the camping style you indicated simply having a pair of good batteries and installing an inverter will allow a few hours of TV daily along with charging or powering laptops, tablets, phones, and other low draw items.
My rig didn't have an inverter installed from the factory either which is actually more common unless your rig was specked for a residential fridge. Inverters are relatively easy to install, just need to decide if you want to power a couple outlets or the whole rig. The more you want to power, more batteries and larger inverter will be required.
The 120Vac requirements stated in your query can be solved by installing a 300 watt or so inverter in your entertainment center, spending a bit more for a pure sinewave model will eliminate any issues powering delicate electronics. A DC power socket might be available nearby where inverter can draw power greatly simplifying the installation process.
We have an onboard Onan that easily powers our rig as if connected to shore power, but is way overkill 90 percent of the time. The first week after purchasing our current rig I installed an inverter and added another battery to power all our A/V equipment when off the power grid. We had pretty much the same camping scenario you indicated in your post.
We only use the genny to power high current items such as convection microwave, AC unit or a couple of space heaters, and hair appliances used by DW and DDs. Usually amounts to an hour or two daily, and thanks to our Iota IQ4 converter restoring consumed amphours into our battery bank is quick and efficient. With batteries happy we are ready to enjoy our A/V system.
We have discovered boondocking and dry camping as are preferred method of RVing and have since added solar to the equation. Other than powering high demand items genny sits idle, under most conditions solar effectively replenishes our battery bank. Although we have roof mounted solar panels we also purchased a suitcase version that delivers max output nearly all day.
