There really aren't any "nice" RV parks near the balloon fiesta. There are a few rinky dink operations in town, but nothing to write home about. Personally, if it were me, I would opt for Coronado State Monument. You can get a full hookup site and it's a nice clean RV campground. You will also have the benefit of shade, which you will be hard pressed to come by at any of the RV parks or RV camping facilities around town.
American RV park isn't too bad and I know a lot of people use it for Balloon Fiesta as they do have a shuttle...but it's not really close to the park itself. They do have some small shade trees on some sites, and the landscaping overall is pretty well done, but for the most part, it's a well manacured high desert parking lot. Never stayed myself, but I know others who have and they have found it to be very clean and nice facility. It's huge with 216 fully hookup sites.
Other options to look at would be the KOA Albuquerque (opposite side of town from the park), KOA Bernalillo (just a bit north of the park and fairly close), or Enchanted Trails RV Park (not near the park and pretty much desert). Another option to consider would be the Isleta Lakes RV park, though it would be a pretty good haul to the park.
You could also opt to stay on site at the park...for the hookups you want, you'd probably want the "President's Campground". This isn't a full time RV park/resort, so amenities are limited...to my knowledge, they do not have restrooms and showering facilities, etc. Little to now shad here.
In that RE, keep in mind that Albuquerque is high desert...there's really not a whole lot of shade available other than being along the river (see Coronado State Monument)...it's just going to be very difficult to come by.