Are there luggage lockers or a baggage check at this station?
Its not always an easy question to find the answer for. I don't remember one but I wasn't looking for one. There is an unoficcial webpage with great photos of the station, and if you look in the table of services it does mention Deposito bagagli. It is at http://www.stazionidelmondo.it/ventimigliastazione.htm Good luck...
Cynthia, I found another link which confirms what Nigel posted. There does appear to be a Deposito Bagagli at Ventimiglia. Have a look at THIS Trenitalia website. I wasn't able to find any information on costs or other details. I assume you'll either be coming from or going to France, as that's the border transit station. Happy travels!