On your first day in the city, take a guided tour of Sanremo, which can take from 3 to 9 hours on foot or by car. These tours usually introduce you to the medieval centre of the city, the ancient quarter of La Pigna, just north of the main street, Corso Matteotti. It consists of many narrow winding streets, side streets, and passageways that retain a medieval charm. Locals can tell you how to get to places of interest, like the Sanctuary of the Madonna della Costa. From there, walk up via Palazzo and see the sights along this street. Chief among them is the ancient San Siro Cathedral (13th century).
The average cost for a group of 1-4 people starts from 30 EUR per hour. Russian excursions in the centre of Sanremo are very popular - a guide will lead you through the iconic places of Russian aristocracy and the Romanov House.
On the other days, however, it's best to take a bus tour from Sanremo. The most popular destinations include Menton (a French border town famous for its citrus groves), Nice, Cannes, the Principality of Monaco and Genoa.