Using a small generator like a Honda 2000i to recharge your batteries takes only 1-2 hours a day depending on how much battery you have. The cost for fuel is almost nothing. Yes, they can run on propane, but I use my portable for other things and prefer to not have to carry around a propane tank. They put out less wattage on propane as well. The advantage is that propane does not age like gasoline.
If you want to power a 13.5K btu A/C you can only really do that with a generator, and for a better experience you will want a 3,000 watt or 2 2000's running in parallel, or a 2,500 watt for an 11K btu A/C. That's going to take a lot more fuel. I used to run my 13.5K A/C on the Honda 2000i but it was super marginal and it would go through the internal tank in about an hour. The A/C was modified with an aftermarket starting capacitor to even make that work.
Running A/C on solar is not practical. Let's say you have a 13.5K A/C that uses 1,200 watts on average. For 8-hours of use that is about 800 amp-hours from 12V batteries. Since 12V deep cycle batteries used in RV's typically max at about 100 AH and you can only use 50% of that without damaging them, you would need at least 8 batteries (assuming they are charging when you are using the A/C), and a solar array of 7 200w solar panels (!).
Solar is very effective if you just need lights, propane fridge, and a moderate amount of recharging laptops and phones. It's completely useless in the shade of course, which is why a lot of us carry a small generator to top off the batteries when needed. A smaller 1000 watt generator is enough for that. The 2000 is needed only if you want to run a microwave or other appliance that uses more power.