Become a MacRumors Supporter for $50/year with no ads, ability to filter front page stories, and private forums.
There is a huge number of ways to save data in iOS.

Instead of saving the notes to the device itself, you might consider saving it to a back end server instead. I would recommend taking the time to get a basic familiarity with Node.js + MongoDB. You can build out your own backend. This way, a user with a single account can see all of their data on all of their devices.

However, if you definitely want the notes to be saved locally, there's a few technologies I would recommend. CoreData can be powerful but it is extremely quirky and difficult to work with. Realm is a newer database framework which I have never used in a production app but I have been experimenting with lately and I like it quite a bit.
 
Register on MacRumors! This sidebar will go away, and you'll see fewer ads.