Yes, La Spezia is somewhat less expensive, but saving a few dollars here would really diminish your Cinque Terre experience. We've gone to CT twice, staying in La Spezia (Hotel Mary) once and in Vernazza (Pensione Sorriso) the other time. Staying within the villages was a much more interesting experience and we were able to pack a lot more into our trip by staying there.
The trains from La Spezia to CT don't run nearly as frequently as you might expect. They're roughly hourly, but some are closer together and some are farther apart. When we stayed in La Spezia, we had reservations for a 2 pm train back to Naples. Our plan was to go to Manarola in the morning, walk the trail above the vineyards, then come back to La Spezia to catch the train. I misread the train schedule and thought that if we missed the 8:30 train, we could catch an 8:50 one. Turns out the 8:50 train only runs Tues-Fri (or something like that-- I'm doing this off memory). Of course we missed the 8:30 train (2 little kids-- it happens!), found out the 8:50 train didn't exist, then saw that the next train wasn't 'til 10:00 or so. This didn't give us enough of a cushion to go to Manarola and still get back, so we really missed out that day.
Find a way to stay in the villages!