There are many ways of seeing both Rainbow Falls and Devils Postpile, and there are other things to see around here, but I'll explain what we did and my rationale. Keep in mind that this is just "the long way to the Bay area" for us so we're already on an extended detour!
Catch the Reds Meadow Shuttle from the "mammoth" sculpture at Mammoth Mountain Inn. Just go to the window at the Adventure Center on the day you want to take the shuttle and buy tickets which are $7 per adult and $4 per child. My recommendation is to take the shuttle all the way to Stop #9 which is the 2nd to last stop on the shuttle. EVERY SINGLE person on our packed (even people standing) shuttle bus got off at Stop #6 to do the Postpile first. We moved to the front of the bus for the remainder of the ride, and our driver gave us a personal tour of the valley. My other recommendation is to SLEEP IN and take the shuttle around noon or 1:00. The rainbow at Rainbow Falls is most colorful in the mid-afternoon sunlight. The hike from shuttle bus stop #9 to the falls is 1.2 miles DOWNHILL. Hello, that means 1.2 miles UPHILL on the way back which is another reason why we thought hiking Rainbow Falls first before Devils Postpile would make more sense while we still had more energy. When you get back up to Stop #9, get back on the shuttle (they come every 20 minutes) and take it to Stop #6 for the Postpile. If you've timed this hike like we did (with lots of photo stops) you will be arriving to the Postpile around 3:30 or 4:00 when the mid-day sun has moved to the west so you can look up to the east and view the large basalt Postpile without being blinded by the sun, and instead the sun will be casting some wonderful light on your Postpile. The hike to the Postpile is only 0.4 miles of flat hiking with an optional steep section of hiking up to the top of the Postpile. When we got back on the bus at Stop #6, we traveled down to pick up the hikers at Rainbow Falls Stop #9, and they were lined up like a ride at Disneyland. Some even had to wait for another bus. Just my thoughts on the subject. The Sierras are HIGHLY popular in the summer so if I can avoid the crowds, I will!
Length: 2.4 miles for the Rainbow Falls section + 0.8 miles for the Devils Postpile section = 3.2 miles of total hiking.
Elevation gain: 335 feet
Time it took us: 4.5 hours from leaving the mammoth sculpture to arriving back to the mammoth sculpture.
Dogs allowed: If they are muzzled and well-behaved then they may ride the shuttle bus.
Fees: Shuttle bus: $7 per adult, $4 per child
Directions: From Hwy 395, take Hwy 203 west up through Mammoth Lakes to Mammoth Mountain Inn where you catch the shuttle.