I don't have permission to post links so I can't show screenshots, but you'll find the times below; you can confirm it in your logs. For the industrious - or skeptical - amongst you, you can find a thread titled "Rares at Fixed interval opportunities (incomplete)" over at the Reddit forum for Fallout Shelter. There are links to screenshots there.
Fixed Opportunities for Rares and at least one Legendary
0230 - Super Duper Mart
0500 - Escaped Slaves
1000 - Drunken Drifter - Appears to only potentially only give money
2000 - Gas Station
3000 - Abandoned Diner
6000 - National Guard Depot - **Opportunity for Legendary**
Hourly Chance at Rares
At some point during the hour, all of your outbound explorers will see a message "I've found a locker containing ". When it happens, it happens for all of your outbound explorers at the same time. Occasionally, this event will be upgraded to "What luck! I found a laying on the ground!" Given the text, I'd guess that may be based on the Luck SPECIAL or it could be completely random; more data is needed.
Potential events at predictable intervals
I hadn't had cause to look for these before so I don't have as much data on them. These are the ones that have been spotted by me and other people on this thread. They can result in experience, caps and common items. No evidence to suggest that they can produce Rares however.
0000 - Broadcasting Tower
0000 - Raiders
0000 - Fugitive Slave
0030 - Ghoul
0030 - Refrigerator
0030 - Wounded Sheriff
0030 - Abandoned Shack
0230 - Talon Company Mercs
0500 - Slaves
1500 - Slave Camp
2000 - Merchant
4000 - Lost Farmer