Beerman two towns that did not make your list was Portovenere (also known as Porto Venere) and Lerici.
Was is to the west of La Spezia and the other two the east by a short bus or taxi ride. La Spezia is a major train hub. I was lucky enough to work there for a month about 10 years ago.
Both places are magical and I think Portovenere would claim the home of Pesto, but who knows.
Lerici has a cool castle and tunnel that runs under it. When you pop out the other side there is great restaurant with a view of the Poet's Sea
Definitely take a look at these two. You can also stay in La Spezia and explore both easily by bus or ferry they run frequently.

Here a few shots to enjoy
And of course you know the seafood is amazing in that part of the world.