All September is normally nice, October you need a little bit of luck. Same in Early summer, May can be a little cold&rainy, but June should be just nice. Dont go around Jul/Aug, it can be hot and the crowds in Cinque Terre, Portofino and the other tourist hotspots will take all the joy out of it!

I ran Cinque Terra point to point in the middle of summer. Amazing. Right now is probably the best time.. all the summer crowds are gone.

Hopefully no bridges collapse under you.

I was there during spring time and it was lovely.
The pesto is good all year around.