If you are only going to be gone for 4-5 days or as long as your batteries will run your refrigerator, you can use the regular airport parking lots. I was going nuts a couple of years ago about what to do with my motorhome while I flew to visit grandkids for five days. The hotel parking lots and offsite parking lots are not always very secure. I finally called the airport and talked to their parking people.
I have left my motorhome at Tampa Airport twice for five days each. They have a fantastic outside economy lot where you can park big vehicles. In fact, the signs driving into the airport will direct you to the "Oversize Vehicle" economy lot. It is paved and well-lit, has tons of space even in busy times, and the parking building shuttles drive past your vehicle all day and night, so it is very secure!! And they only charge you $9 a day, just what they charge cars.
I also left my motorhome at the Las Vegas Airport for five days, although I think I was in the wrong RV lot--they have two and one is bigger, but I was in the small one. People pulling trailers had parked wrong, so I had to park wrong also. Anyway, we all managed to get out and my vehicle was safe when I got back.
In April 2016, I am going to leave my motorhome at the Salt lake City Airport. Called them and they assured me that had plenty of spaces for big vehicles right in the regular economy outdoor lot.
Anyway, all three times I left my motorhome at an airport, refrigerator was fine and battery still had some charge left to run refrigerator when I got back.