I'm also in the camp of not going with Propane. You use it up quicker, it's harder to obtain, and most dual fuel generators have slightly less output with propane.
For a 2000 watt generator occasional use I'd go with the Champion 2000 watt inverter. It's 90plus percent of Honda in quality and ability but can be purchased new for around $500 on a regular basis which is half the price of the Honda.
Personally I'd forgo the above mentioned generator and purchase the bigger Champion Inverter (3100 or 3400) They start at around $700 dollars so you're looking at more than it appears you wanted to budget, but one of these will give you the option of running your AC. Since you didn't mention when you were traveling this might be something worth considering since it gets pretty Hot in much of Southern Utah in the summer months.
Good luck on the trip, Utah is a great place to explore.