From Nice, Ventimiglia can be reached by the SNCF (the french railway company) train that also passes through Monaco. The adult fare from Nice is € 6.40 for adults / € 4.80 for youth (12-25 years) (as of August 2010). To purchase tickets here, you will need the amount in coins or an EC/Maestro debit card.
The "new" town center and shoreline are an easy walk toward the south from the terminal. The original/historic section is across the river to the west...also an easy walk.
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 "new town" has a decent selection of storefronts offering quality goods at some savings. You'll find decent bakeries/pastry shops everywhere, but for better mercantile, you should venture a few blocks away from the train station.
The covered market opens every day except Sunday, offering seafood/meats, fresh vegetables, fruits and locally/regionally-made sauces and jams/jellies.
On Fridays, the "big market" comes alive. Stretched many blocks along the shoreline on Passeggiata Cavallotti in the new town, vendors hawk rather repetitive offerings of often counterfeit goods...clothes, purses, shoes, etc., at very competitive prices (after bargaining). Savvy shoppers occasionally find genuine, unbranded bargains...sometimes well-made in Asia.
If visiting by car on a Friday, parking can be difficult to find.
Travelers entering France by car from the direction of Ventimiglia are frequently questioned by police at the border about counterfeits; much less often, westbound trains stopping here may receive similar screening. If found, counterfeits will be confiscated, and you'll likely be levied a major fine.
The train terminal contains an indoor buffet restaurant that enjoys a decent reputation for its food and cost. For more sophisticated offerings, try near the seashore in the "old town", e.g., Pasta & Basta.