sorry for grammer, just writing this quickly.
I just wanted to write a response, just in case anyone else is reading this. Nobody at the Apple store really knew the answer I had to figure it out for myself.
My old iphone had a lot of software issues, it was then transferred to new iphone. I had to restore new iphone in order to get rid of the bugs. Also some of my notes, of course the most important ones, were not transferred to the new phone at set up. I was told to email the notes from old iphone. Well, the old iphone was not restored yet and still had problems so the emails were lost in the ethers, who knows. I didn't know until next day, should have checked email on the spot to see if sent. Anyway, so thinking they were emailed, we restored the old iphone to original settings, with most icloud data transferred, (EXCEPT the important notes, for some unexplainable reason, I've been trying to get on chat for two hours online, something must be wrong with their system, so I still don't know why, I think it's some type of glych.)
I followed some advise below, but to no avail.
I then did what the technician at Apple store advised, to restore the iphone while plugged into pc. I did that, still the important notes weren't transferred.
Now this is so weird and makes no sense,
-after restoring iphone while plugged into PC (I do not know if the restore was even needed to execute the following...so try doing it without first)
-in Settings where it lists icloud, mail, notes, reminders, phone, messages, etc.
-I clicked on Notes
-it had two selections: icloud or gmail, so weird because hotmail is technically my main email. (Again, the "mysteries" of Apple ensue)
-where it said Default account, gmail was checked. hmm, gmail? that's weird I thought
-so I switched it to icloud
-when I went back into my Notes all the notes were magically there.
I have no idea how or why, but finally at ease....
I hope this can help somebody out!
Good luck.