Mid-July is not at all too late for wildflowers in the high meadows at Mount Rainier. Your timing should be just about right for flowers up at the Sunrise area. At Paradise, the best known area for wildflowers, the bloom is typically at peak sometime during the last week of July or first week of August. The view of Mount Rainier from Reflection Lakes should also be prime then.
Christine Falls and Narada Falls are short walks from well-marked pull-outs between Longmire and Paradise. Myrtle Falls is an easy hike from Paradise Lodge.
Cougar Rock Campground is a great base for many good photo locations on the south side of Rainier, but it's a bit far from Sunrise. If you have any flexibility, you might want to move to the White River Campground for one night so you'll have a much shorter drive to be at Sunrise at sunrise.
Mount Rainier is awesome - have a wonderful trip!
- Greg