You should be able to capture lots of pictures of wild flowers. There
are lots of trails behind Paradise that will get you real close to the
mountain. Myrtle Falls is an easy walk, but the rest of the trails are
a bit much for an out-of-shape geezer like me. The lodge at Paradise is
closed while they remodel it. And the parking lot up there doesn't hold
that many, so I'd get there early in the day.
Reflection lakes are easy to get to and close to Paradise. As for time
of day...just point your camera just about any time and you'll get some
pretty spectacular scenery. There are lots of waterfalls along the road
too on the way up from Longmire.

I've got some Rainier pics on my Web site:

http://users.techline.com/randya

What type of photographs do you want?  How far do you plan to hike off
the road? Where are you staying and how far do you plan to drive?

The circumnavigation road will be open with lots of scenic viewpoints
and trailheads. August is also the peak tourist season, and very
crowded, when and where parking is restricted once the lots are full.
There are lots of excellent guides to Mt. Rainier NP where you can get
ideas, check bookstores or Amazon. Check past posts (here) and through
Google to find links to Web sites.  And there are several Web sites for
information from the USGS and NPS along with a USFS-NPS information
office in downtown Seattle (REI store).

Without more information it's hard to recommend places.  There's just
too much to see and photograph.

Get up early and drive to "Sunrise" before sunrise, and you might get some -really good- shots of the mountain in early light.  (The time I tried it the weather didn't cooperate, and then I ran out of batteries, and had to drive back to Enumclaw to get more batteries.  There were probably a dozen photographers on the mountain at that time, and several of them searched their own equipment bags to see if they happened to have the right batteries, which I -really appreciated-.)

            dave

The midday sun that doesn't do so well for vistas can be avoided in the
woods.  If you've never seen what the folks in the NW call "old growth
forest," you'll be amazed.  Get into the old, old forest and bring a
tripod - the midday sun doesn't get thru very well.  NPS web sites will have
descriptions and maps of the trails.

Bob in Las Vegas