Yes, +2 on Ken's suggestion. That is probably the best on-trail route in the area!
Get yourself an Ansel Adams Wilderness map; or Tom Harrison's Mammoth High Country map so you can follow this discussion:
Your start/end point is Agnew Meadows. Not sure if the summer shuttle from Mammoth Lakes will still be running there; but you can drive directly to Agnew Meadows and park there. From Agnew Meadows, there are three ways to hike to Thousand Island Lake on your first day. I highly recommend taking the so-called High Route (Pacific Crest Trail). That route is famous for its fall colors! And it will give you a magnificent view across the valley to the country you'll be seeing the next day.
From Thousand Island Lake, you'll head south towards Garnet Lake. There are two ways to get to Garnet: The easy way (John Muir Trail); or the off-trail way ("saddle") mentioned by Ken. The off-trail way is not hard; it's all Class 1 hiking, and straightforward navigating. The benefit is that you get real-up-close to Banner Peak, and into a gorgeous little lake valley above Garnet Lake, that you'd never see from the JMT. It does add some time, though, so if you want to do this, be sure you're up for a long day (especially if you want to get all the way to Ediza), and get an early start. For the off-trail route, walk along the north and then west shores of Thousand Island Lake. Head for the obvious low saddle due south. Descend to the lake basin above (west of) Garnet Lake.
From there you will want to get to Ediza Lake. Again, there are two routes: On-trail and off-trail. I don't recommend the off-trail route, as it looks like a long, steep, and difficult slog; but someone here might disagree with me. To go the on-trail route, drop east to Garnet Lake, and then follow along the north side of Garnet Lake till you hit the John Muir Trail. (The terrain does not allow you to follow Garnet's shoreline at lake level; you will be about 100-200 feet up.) Follow the JMT south to the junction with the Ediza Lake Trail, and go up to Ediza. Camping at Ediza is in some trees on the north/northwest shore.
On the final day, it's a straightforward hike from Ediza Lake back to Agnew Meadows.
Thousand Island, Garnet, and Ediza Lakes are considered by many to be among the most scenic lakes in all the Sierra. I wouldn't disagree. Most Sierra lakes this spectacular take several days to hike into, but you'll be able to see them all in just 3 days. You're lucky to get to see this country in the off-season when it is not overrun.
Bears are very active at Thousand Island in particular; watch your every move! (Do not leave your food unattended even for a few minutes.)
Personally, I don't find the Devils Postpile all that interesting. It was kind of a letdown after all the amazing lakes. You park your car, walk the short dusty trail to the Postpile, take a couple of pictures, and then hurry back to your car so you can get started hiking to the real stuff. In any case, don't build a trip around seeing Devils Postpile.