The obvious day trip is the rest of the Cinque Terre — Riomaggiore is 10 minutes south on the train, Corniglia 5 minutes north, then Vernazza and Monterosso. The blue trail (Sentiero Azzurro) between villages is the classic walk when sections are open; otherwise the train moves you between them in minutes.
La Spezia, the main port city at the eastern end of the line, is worth a half day for its naval museum, the Sunday market and the better restaurant prices.
