I have a Yamaha 2000EIS and love it. It's smaller than the one you are contemplating but of the same brand so I'm sure the quality carries through.
Keep in mind that the while the 2400 will run your AC, you will have problems if any other significant electrical draws are present. House lights should be fine but watch out for microwave, water heater (gas OK, electric no,) fridge (force to gas,) hair dryer, etc..., you get the picture. The 2400 will work safely for the AC but is close to the limits of it's capabilities when powering the AC so be careful.