Hi Larry,
I was really happy with Riomaggiore. I found a place through Mar Mar, which is an agency that rents out private apartments in town (they also have a cleaning staff and the places were kept nice and clean). You can fill out their accommodation request form with the date, and they will email you with the price of each available place, along with a realistic description that includes how many stairs you must walk to get to each one.
As for the best town, I would suggest that you ignore Corniglia simply because it is a long hike up all those stairs from the train station. You will not want to get around so much if you had to walk them all the time.
I personally preferred Manarola and Vernazza, but they are smaller towns than Riomaggiore. Riomaggiore is the second-largest of the CT towns. One of the nice things about it is that the easiest (and shortest) section of the hiking trails runs from Riomaggiore to Manarola. If you stay in either one of those towns, you can easily stroll along the Via dell'Amore and watch the sun set. Obviously you can do this if you stayed in any other town, but then you would need to take the train back after.
That being said, Vernazza is usually the most sought-after town as it is the one preferred by Rick Steves, and I agree that it probably is the most picturesque of the five.