electricity at the campsite

I would say most campground catering to short time visits do not charge extra for electricity. Places for long term stays are probably a separate story. 

A lot of campgrounds do not allow generators due to noise. Those that do may have specific hours that you can run them. You have to determine what you want to power with a generator. If you want to run the AC, then it needs to be big enough for that. If you just want to get your battery charged and run some lights and stuff, small one would do. A LOT of things in a camper run off 12V, your battery. So keeping battery chagred is your 1st prioity. 

Lots of factors at play here. Where are you camping and for how long? A lot of State parks will not have electric at all sites, most private CGs will have electric at every site. If you plan a vacation, it's likely to be included. If you are long term, then they may put a meter on your site and pay separately. What are you camping in? A tent requires no electricity. A small TT requires a small amount, a large FW or MH can require a lot of electricity. Usage depends totally on what you want to run, and the amps required to make things run, and what appliances run on what and what equipment you have. If you have a bare bones TT with one battery and no inverter, then you will probably not last long running lights and a TV etc. on one battery. If you have multiple batteries, solar and an inverter you could run things for a while. If you have a generator built in or stand-alone you can run it during a CG's dedicates hours for generator usage. Your fridge may run on multiple fuel sources (LP, 12V, 120V, shore power only or inverter). I suggest you familiarize yourself with your Rv and equipment, find out what runs on what, what you want to use and the amp hours required vs how much capacity you have. Some things run on 12V and some things run on electricity - either batteries and inverter, shore power or generator. In any case you will need to recharge your batteries. If on shore power they are constantly being charged. If you have solar it's usually only enough to keep them topped off in storage, if recharging with a generator it can take several hours. 

In Summary, your question depends completely on what RV and equipment you have, from batteries to appliances, where you are camping and what you plan on using while you camp. 

You can look up campgrounds online and see the cost for a campsite with and without electricity; per day. The long and short of it, all things considered, it will never be cheaper to use a generator or any other “power source” then to get a “site with electricity”. The one caveat being, if you are real stingy with power you may get up to 3 days be running off the battery. But that would mean no microwave, no air conditioner, and a marked increase in propane use and a marked loss of battery longevity. After the 3 days your camping trip is over and you would need to go back home and charge up the battery - wash and repeat.

This depends on the length of camping time. Of course, you can also build a solar energy system, but it can be difficult for beginners. For short-term camping, portable charging stations or lithium batteries can be used.

lots of way to do this, if you treat the trailer like a tent with a stove and use very little power, you could get away with no power and a couple good batteries.  My forst trailer was a 28 foot and we were very stingy on power.  with for 6V batteries I could easily got for 2 weeks in the summer, but all we would use for power is the lights in the camper pretty much.  when I got my 5th wheel I got solar put on and transfered the 6V batteries from the camper to it and now I never have to worry about power, but I don't use the AC and I still watch my power usage limiting the kids to 1 movie a night and I use the keurig in the morning and after supper, and limited microwave of 10 min a day.  this also includes the furnace in the fall.  

now if you have a 12V only fridge that adds another factor as they require battery power so a good battery bank is going to be essential

so you have options, and they depend on your power usage and what you want to run.  if you want to run the ac either get power where you camp of get a generator (I hate generators, but cost wise it is the cheepest option when your talking about AC usage), but you have to watch for rules goverening generator usage.  up here you get 2 hours in the morning and two hours around supper, and that is shrinking every year in atempts to phase them out.  If you can live with out the AC then solar is a exelant choice,   if you are a handy guy and you can install it your self you can have a awsome setup for under 600 bucks plus the cost of your batteries, but you should get good batteries no matter which way you go.