On reboot system asking for keychain password for local items

Solution 1:

Keychain password & login are only the same until you change one, then you need to change the other separately

Source: OS X: Keychain Access asks for keychain "login" after changing login password

Note: This doesn't happen if you change your account password using Accounts preferences.
If you want your default keychain to be unlocked automatically when you log in, synchronize your Keychain Access and account login passwords by doing this:

• Open Keychain Access (you can get to it by choosing Utilities from the Go menu in the Finder).
• From the Edit menu, choose Change Password for Keychain "login."
• Type the former password of the account that you are currently logged in to, then click OK.
• If you entered the correct password, a new window appears; enter the original password again in the Current Password field.
• In the New Password field, type the password that matches your current account password.
• Re-enter the newer password in the Verify field, then click OK.

Solution 2:

I am amazed how much hassle changing my Apple ID password causes me, but the solution I've used for this is from Npalamidis on the Apple forums:

1.- Opening KeyChain app
2.- Locking the Keychain by clicking the lock on the top left corner.
3.- Unlocking the Keychain, as soon as I typed my Admin Password it asked me to "Reset my iCloud KeyChain" I clicked yes because I didn't have setup my icloud keychain yet.
4.- Restart computer.
After performing this steps the computer restarted flawlessly and without asking for the "Local Items" password.

I locked and unlocked all the keychains because there wasn't one listed called "local" but following Tetsujin's answer I'll try just the login one next time.