I am looking for cases where local conventional wisdom might suggest a certain route between points A and B, but Google Maps/Waze/other navigation systems or even just personal experience would suggest a different routing.
One example near me: Bay Towne Plaza to the rest of Webster and points east (https://www.google.com/maps/dir/Webster,+NY/Bay+Rd+%26+Empire+Blvd,+Penfield,+NY+14580/@43.2003027,-77.5157264,13z/data=!4m14!4m13!1m5!1m1!1s0x89d6c8e1d0b4f11b:0x1c61f9c26932b681!2m2!1d-77.4299939!2d43.2122851!1m5!1m1!1s0x89d6c965487ac3c9:0x9a81db3c1ab80360!2m2!1d-77.5038997!2d43.1898805!3e0!5m1!1e1?entry=ttu). Conventional wisdom assumes Ridge Rd is the fastest route because it's the shortest, but Ridge Rd is only two lanes and has a bunch of stoplights prone to creating backups, so between 8AM-8PM it's usually faster to take Bay Rd to NY 104.
Between Lemoore and Monterey most map services will mostly tend to suggest CA 152 across the Diablo Range. The reality is that CA 198 is always consistently faster (and shorter) due to the lack of traffic.
From Boise to Coeur d'Alene, the most direct way is US-95 (via ID-55 or I-84) all the way up. That way also feels most intuitive, because you can stick to one highway (US-95) almost the whole way. But time wise, it's roughly tied with taking I-84, US-395, and I-90 in Oregon and Washington, despite that way being 70 miles or so longer. Google sometimes suggests some off the beaten path routes between Pendleton and Pasco, but the "easy" way is I-82.
I prefer using 95 personally (it's not a boring drive), but one time I had a cold, wasn't feeling 100%, so I took it easy and stuck to the freeways. If I'm being honest, it felt faster. In winter I'd also recommend sticking to the freeway, unless the Blue Mountains in Oregon look particularly bad (but if they're bad, 95 is probably bad too).
Between Canton OH and points south of Washington PA, Google Maps suggests using I-79/PA 576/US 22/PA 18/PA 168/US 30 which has tolls and lots of miles of not-great 2-lane road because it is the shortest distance. Most people opt for I-79/I-70/I-77, which is within a minute on time estimates but 38 miles longer.
The Tollercoaster Express Lanes on I-75 NW of Atlanta have a lower speed limit than the general purpose lanes (south of I-575). Express lanes are posted at 55, while the local lanes are posted at 65. Yes, this is obviously due to design speed, but still surprising how this is the case.
While most of the time when you'd want to use said express lanes the general purpose lanes would likely be traveling at far below 55, all the other times you'd effectively be paying more to go slower, at least legally... :-P
On a similar note, are there any more examples where express/HOV lanes have lower speed limits than the local lanes, at least for an extended period?