Depending on what you want to run with the A/C running, you may be able to get by with a 2000 watt unit. While the 3000 watt Honda is a nice generator (I have one...runs my whole house when the power goes out; everything but the water heater and stove-they're 240v) it is heavy (remember I have one!
). The Honda 2000 will run your 13.5k btu A/C unit and other appliances if you don't try to have the A/C on and then fire up the microwave while your wife is using a hair dryer...
The 2000 model Honda (and "blue" Yamaha) are very popular models with RVers. Modest weight (~80 lbs), very quiet, very reliable. Many RVers will use two of them in parallel (they make kits for that) instead of the one heavier 3000 watt model. The 2000, is, of course, more fuel stingy, and if they don't need more current than one will provide, they leave the second one off...if they need more "juice", they can fire them both up. Most, though, can get by with just one 2000 watt unit if they are mindful of current usage.
There are several sites on the internet that list the normal current requirements for various RV type appliances if you want to sit down and actually figure out your current requirements for various scenarios.
Just more food for thought...