Mt Rainier is a glaciated, active volcano, whose summit at 14410 ft is center of Mt Rainier National Park. Three roads provide access to alpine zones. From Chinook Pass on the east boundary, the Naches Loop trail is good moderate walk for flower spotting. From Sunrise visitor center, on the eastern interior of the park, the trail to Burroughs Mountain is a favorite with the best chances to see the most diverse alpine species including arctic willow and moss campion. Paradise on the western interior is famous for its masses of colorful subalpine flora. A forth entrance in the northwest (Mowich Lake) ends in trees-- one must hike in from there to see the flower fields of Spray Park.
There are two species endemic to the park and surrounding areas: Castilleja cryptantha (a drab little paintbrush) and Pedicularis rainierensis (a lousewort with yellow, banana-shaped flowers). One plant species is named for the mountain itself: Rainiera stricta (tall, something like a goldenrod, very common at Rainier but also found south into Oregon).
Depending on the previous winter snow, the best time to visit is often mid-July through August. The park is about a two hour drive from Seattle.