https://tasks.org/ - Sync is optional

You could try loop habit tracker on android. Fully open source. It wouldn't be great for one off tasks, but regular stuff, it would be perfect

https://github.com/iSoron/uhabits

Foss app "Tasks" is the only good option and is very much customisable. You can create tasks and subtasks in it and then create widget of that task.

You can also use google tasks, if you want more convience.

If you want a clean FOSS habit tracker, I can highly recommend Habits:

Habits (Habits is an app for tracking and helping to maintain good habits.) https://f-droid.org/packages/com.willbsp.habits/

I've been using Memorix for years, and have no complaints. Light weight, backup and export features, color coding, repeatable reminders, and you can attach photos if needed. OTOH, not open source afaik.

The checking things off will persist though; for daily things that I want to repeat I manage them in the notifications tray instead of in the app.

On play store: https://play.google.com/store/apps/details?id=panama.android.notes&pcampaignid=web_share

Microsoft's To Do app is good for that. Free and no ads, and at least for now remains focused and unbloated. It syncs via your Microsoft account, but I think it also can work offline without one.

Markor for notes + todo + plans.

Stores things in plaintext in well known formats like md,todo.txt,orgMode,etc

Works grt across platforms with syncthing and few vim plugins.

CalenGoo is a calendar app that can do both events and tasks. It has extensive customization of the views so you can arrange things however you want. Also has a dedicated tasks-only view which I've configured to show upcoming tasks. You can set periodical reminders, check off the tasks, mute them etc. It works with Google account as well as standard CalDAV; CalDAV can be used both via Android (using another app like DAVx5 to do the sync) or by CalenGoo directly; or if you're on iOS it's supported by the OS directly.

If you want to have todo list/notes with checkboxes and don't ~care about~ want any online functionality, I would suggest using Another Notes. Also, I uses p!n to show my todos-of-the-day right inside the notifications.

Edit: I mean "don't want", not "don't care"

The account required for my notes app is just so I can sync between phone/computer, which personally I really appreciate.

If you already have a google account just use Keep and make a checkbox note. It doesn't require internet and it'd just be using another account you already have at least.