It is a big industrial port city. Not the most beautiful city in Italy, in my opinion, but it has a few things to offer to the visitor.
My preference would be to stay in a smaller quaint town on the coast, of which there are many.
The town you are referring to, starting with a C, is probably Camogli or maybe Chiavari.
If you don't care to stay at the Cinque Terre and if you like quaint small towns, may I suggest Moneglia?
It's one of my favorite villages on the Eastern Ligurian Riviera. I thought it was because of memories from my youth, but it turns out that Moneglia made the list of the Most beautiful villages of Italy in the Borghi d'Italia website, so I'm not alone.
Moneglia is about half way between the Cinque Terre and the Genova area (which includes Portofino and Camogli). You are basically less than half hour train ride from all the places you want to visit.