There are a few recommendations for the PineTime in this thread. It is a great privacy focused smartwatch, but I don't think you would be happy with it based on your requirements. It is not a device that allows you to go for a run and keep your phone at home.

The storage on the device is extremely limited, which prevents you from playing any audio (eg songs, podcasts, etc) directly. The device does not have any wireless connectivity (outside of Bluetooth) so it cannot stream any audio either. I'm not certain if you can even connect it to wireless headphones. It does not have any speakers either.

The watch has some apps, but there are no apps that are well suited for fitness. It does count steps well, but it does not directly calculate distance, pace, etc. It also does heart rate, but, currently, the watch screen must be on for it to record the heart rate. I think the longest the watch screen will stay on for is 30 minutes without any interaction, which may be too short for long runs or bike rides. Additionally, I'm not aware of any GPS/location tracking functionality.

Lastly, since the apps are limited and there is no advanced wireless functionality, you can't use it for things that you may be used to for on the go activities. For example, you won't be able to use it to pay for a drink half way through a run or call someone if you hurt your ankle a few miles from your destination.

With all that said, I still highly recommend the PineTime as a privacy focused, FLOSS, smartphone companion, smart watch. I don't think you'll find these features in any other device, particularly at this price point. However, you will be extremely disappointed with it if you're getting it so you can take it on runs while leaving your phone at home.