We've had this dream to go hike between the towns of the Cinque Terre when the weather is nice, after ER and while we are still young enough to enjoy it. Sadly, I am not sure there is an intersection point that doesn't include overcrowding.
Do it - it is worth it - go during the week and avoid the weekend. We hiked it in a day - it wasn't too long of a hike. Pick one of the smaller cities to stay and then just hike or train to the bigger ones if you want another restaurant or experience. Rick Steves has some great advice as well - watch his show or read the book.
The only overcrowding I saw was at the beginning and end and it was mostly Italians. In fact, I'll never forget the young lady in stacked sandals on the hike going slowly and talking a mile a minute. I was shocked at her attire as it wasn't the best for the hike (especially the shoes). It reminded me of the people trying to climb Half-dome in flip-flops