Hopefully, you have seen enough to stop using RailEurope for your rail planning. The German train website www.bahn.de if by far the best in Europe for planning your rail trip. Somehow, they have taken the time to incorporate schedules from most of the different train systems in Europe. It's really the best. Unfortunately, you can't buy the tickets from them unless your trip originates or ends in Germany or Austria. Let's look at a few things. First, here's what Bahn shows for June 5 from Milan to Nice Ville (the train station you want). http://gyazo.com/1b5e8d4fdd8ff82b50047af2cdaab4f0 Notice that there is not a dearth of trains. You do have choices. First, you will be taking an intercity train from Milano Centrale to Ventimiglia. Ventimiglia is an Italian border town where you change to the French trains. The Trenitalia trains do not go into France (at least not yet they don't). Then, you take a 47-minute ride on a French regional train to Nice Ville.
Next, here is a snapshot of the train schedule from Nice Ville to Torino Porta Nuovo on Sunday, June 8. http://gyazo.com/7566fb10f57b98ab205bea18eacd0d7a It's a bit longer trip as you are coming 1/2 way back to Genoa to Savona and then routing NE to Torino. The transfer point differs on these runs so while on Bahn, just press the red button on the left and the routing will open up.
Now for tickets. No big worry here as the trains are either Italian intercity trains or regional trains. Regional trains are like your local bus system. You can walk up, buy your ticket, validate it to make it active and then jump on board. No seat reservations ever. No discounts either so you can easily buy the tickets there as you need them. They don't sell out either as you can stand if there are no seats. Again, it's like you local bus or light rail system.
For the Italian intercity trains, you do need seat reservations. And, you can buy these tickets in advance from www.trenitalia.com You can buy non-refundable discounted tickets for these runs. Regular base fare from Milano Centrale to Ventimiglia is 30Euro but you can get the discounted fares as low as 9Euro. Here's a snapshot that shows most of the train runs for June 5. http://gyazo.com/f6eb3124c682b330ceac21bbb1349cae
So here's my suggested travel plan if you wish to purchase the discounted tickets. If you don't, you can wait until you get to Milan to buy them.
1) Go to www.trenitalia.com Purchase one of the runs shown above for 9Euro from Milano Centrale to Ventimiglia (use the Italian spelling I have shown). Unfortunately, Trenitalia will not show you the run to Nice. When you get to Ventimiglia, buy your ticket to Nice Ville. Don't worry. Plenty of trains.
2) Here's a snapshot of the June 8 schedule from Ventimiglia to Torino (not Turin). http://gyazo.com/8c7b821fb8251af79831259b023e5003 Not too much of a possible discount but you can purchase most of the runs shown. For the runs with all regionale trains, Trenitalia will not sell you these tickets online more than 7 days out from the time of travel. I've looked and the fare for the 10:30 run is 11.85Euro. If you want this run, you can buy it at the station in Milan before you depart for Nice. Another nice feature of buying regionale train tickets while in Italy and not online is that they are good for 60 days. No train information is shown on the tickets. Just the 60-day date window, point A, point B and the class 1st or 2nd. When you are ready to depart Nice, just buy your ticket to Ventimiglia. At Ventimiglia, you will need to board only a regionale train from Ventimiglia to the Point B shown on the ticket. Do not board any of the intercity trains. Your ticket won't work there. Be sure to validate all regionale tickets.
