Surprised to see Obsidian not being the top recommendation, I switched to it recently and am loving it. I use SyncThing to sync my notes between all my devices for free.
You can use obsidian to just edit files on disk and handle syncing yourself (eg. With Nextcloud, syncthing, Dropbox)
The company explicitly says you can sync obsidian notes by yourself if you so wish. They offer a paid version but under the same conditions as everybody else. I also use SyncThing like the other person who replied and it works great. I really dig Obsidian.
If you have to sync by yourself, every text editor is "close to Google keep".
False
SyncThing works very well for Obsidian and is completely self hostable.
Although SyncThing on iOS isn't as nice as on Android.