From Nice it can be reached by the SNCF (the french railway company) train via Monaco. The adult fare from Nice is € 6.40 for adults / € 4.80 for youth (12-25 years) (as august 2010). For the tickets you will need the amount in coins or an EC/Maestro debit card. Beware that in Ventimiglia the automats are often out of service.
Ventimiglia has an awesome medieval old town, which is not meant for tourism but rather a place where normal inhabitants live. It has also a beautiful view of the beach in its highest point.
See the remainings of a Roman theatre (century 2nd ) and the traces of the ancient city walls. The ruins of the ancient Albintimilium are situated in the plain of Nervia, c. 5 km to the east of the modern town.
Go to swim at the beach!
The town has a decent selection of storefronts offering quality goods at some savings.
On Fridays, "the market" comes alive. Stretched some two kilometers along the shoreline on Passeggiata Cavallotti, vendors hawk rather repetitive offerings of often counterfeit goods...clothes, purses, shoes, etc., at very competitive prices (after bargaining). Savvy shoppers occasionally find a genuine, unbranded bargain...often made in Asia. Travelers entering France by car from that direction are frequently questioned by police about counterfeits; occasionally authorities on trains stopping here may screen for them also. If found, counterfeits will be confiscated, and you'll likely be levied a major fine.