I've been going to Mt Rainier for 40 years, in tent, pop-up, and fifth-wheel. Most recent visit was last August. It's a LOT more crowded than it used to be, especially on weekends when you get day trippers. The Ashford area, Parsdise and Cougar Rock have become extremely congested. You may have luck in the campground at the southeast end of the Park, near the Ohanapecash visitor center - the Seattle crowd usually does not go that far east.
Wildflowers are abundant on the trails around Paradise Lodge.