+1 for Google Keep.
It has a resizable home-screen widget which displays notes. Accross the top of that widget is a menu bar with 4 icons:
1 - Note icon
2 - Checklist icon
3 - Microphone
4 - Camera.
Clicking either of the first two icons of that homescreen widget and keyboard is open with soft keyboard displayed ready to type (in a freeform note, or a checklist). That's what op wanted.
If you don't want to take up a lot of homescreen space, you can resize that widget to one row by four columns... so it only shows those four icons, not any notes.
But there's a lot more....
That clever microphone. It's a HUGE benefit. Tap the mic and of course you can speak a note. The note gets saved with:
1 - a text-to-speech transcription (writing showing what it thinks you said)
2 - an attached recording (in case the text to speech transcription doesn't make sense when you read it later, you can listen to the audio if you need to in order figure out what was actually said and manually correct the transcription).
AND it can be done off-line (at least in 4.1+).. the Google text to speech engine is now built into the phone and doesn't require data connection.
I use it a lot when I'm driving (carefully) to catch things that pop into my head.
All I do is tap that icon and say what's on my mind.
When I have more time later, using either computer or phone I transfer most of those notes into Tasks. Keep has a PC "program" and a phone app both provided by Google. Tasks also has a google PC "program" but no phone app...there are plenty of 3rd party apps and I use GTasks phone app to access/update the same data on my phone. Gtasks is a great organizer. When I transfer items over from keep to tasks, I assign the item a category, urgency, and reminder date and sometimes a reminder time. . Gtasks allows to browse a list of all items in a category, move them around for user-order, re-sort them by reminder order. Also a list of all category tasks sorted by reminder date. Gtasks has a search feature which is oddly missing from the Google PC interface used to access Tasks. Gtasks also adds the time and priority to the reminders (the Google side has a reminder date, but not a time or priority). In summary the Google Tasks itself is a little coarse, but the GTask app makes up for it well.
Sometimes when I'm on the road I turn my data connection on and use Google voice commands. Can call, text etc handsfree. Aslo my Google voice command "note to self" command is set up to go directly to Keep (where again it stored transcription and recording). It uses a little data, but requires no fumbling with the phone to get to that widget.
