My wife and I were in San Remo for a week in '04, and we had a great dining experience at La Volta Buona?. The owner, Matteo, was an extremely friendly and ethusiastic host; he went through the menu in detail and explained the preparation of each dish. The next week of our trip, we met a French couple (who lived near San Remo) in Venice, and we told them we came from San Remo. They said that La Volta Buona was their favorite place there and that Matteo was a friend of theirs.
Nuovo Piccola Mondo was also very good. In our journal, we wrote "very high-end, fresh food - delicate in preparation." Our French friends weren't familiar with it; I think because it was fairly new in '04.
Both places serve similar Ligurian dishes (trofie al pesto, etc.); the main difference being that La Volta Buona? takes a more casual, traditional approach.
Also, if you happen to be in La Pigna (the old town), stop by Bar Mazzini for a beer. The couple that owns it are very nice, and the local patrons are friendly and will strike up a conversation with you.