Olympus Tough Cams. Not the best at anything, but the best overall package for hard use conditions like cycling, hiking, camping, etc. I have all kinds of compact and midsize digicams, including some excellent Nikons and Ricohs. But for bike rides if I take anything besides my phone, it's an Olympus Tough Cam.
I despise phone ergonomics and won't use my phones while riding. Drives me nuts when other cyclists juggle their phones, dropping them and endangering everyone around. But I will use a compact digicam while riding -- with a neck or wrist strap. I literally point and shoot, no looking at the rear screen. I've done it for so many years with various cameras I usually need only minor edits to straighten the framing.
Mine is an early model low end Tough Cam, JPEG only, so it's strictly snapshots. Good in camera selections. Better than my phone JPEGs, but no room for editing to improve low light noise, etc. Eventually I'll get a higher end Tough Cam with raw files.
To get better image quality, go for a Sony 1-inch sensor digicam, or older Nikon CX format like the J-series or V-series. But the Sony is more compact with better image quality in a mid-size sensor.
In a DX or crop sensor I'd go for a Ricoh or Fuji. But those are pricey and relatively delicate for bike cameras in a jersey pocket.
And if you're interesting in video, don't waste time and money on cheaper or more expensive cameras: Get a Drift Ghost X for a 1080p camera costing less than $100; or Drift Ghost 4K if your computer can handle the editing burden.
The Ghost X includes a 5-hour battery pack, streamlined and reasonably weather resistant (mine withstands moderate rain without a protective shell), easy to operate, pretty good phone app to check videos on the fly. And there's an optional 8 hour battery pack for only $25-$30. Can't beat it for only $80. I've used it every ride for a couple of months, not a single hitch that wasn't my fault (forgetting to turn it on, or not listening for the confirmation chirp).