In Notes app I have some notes stored: On My Mac
my share menu though only gives me the following choices:
when I click More…
AirDrop is selected and at the top!
Mail and Messages shows up, but no AirDrop.
How can I AirDrop my Notes from mac to iDevice?
edit: already fixed in macOS High Sierra.
Best Answer
It appears that you cannot share notes via Airdrop from a Mac.
I have checked four Macs (all running either El Capitan or Sierra) and in each case I find the exact same situation as you. More specifically, trying to share a note does not give me the option of using Airdrop and if I click on the More... option I also see AirDrop listed with a ticked checkmark (greyed out just like in your screenshot).
This is not something I had noticed previously as I haven't tried to share a Note from any of my Macs.
Now, I also checked whether this is a known issue and found this discussion on Apple's website. Although it was started in January 2015, you'll see that the most recent post was (at the time of writing this) just over a week ago.
I'm not entirely sure why sharing notes via AirDrop from a Mac isn't an option (although the fact that notes are all stored within the Notes app and can be synced via iCloud may be part of the reason).
I suggest you send feedback to Apple.
If you do need a way to share your notes via Airdrop, then there's a few workarounds online (including within the above-mentioned discussion). The one I like most is to do as follows: