Nice (Castagniers les Moulins) - evening out in Monte Carlo

My son and I are going to be in France mid next week. We are 'stuck' on a tour bus, and will be checking in to a hotel in Nice Tuesday evening, March 11th (not sure the time, may be a wee bit late). We are planning on breaking away from the group to find our way to Monte Carlo for a visit to the casino.

Any advice on how we can get to Monte Carlo? We won't be able to drive, and although I prefer reasonable cost options I am pretty wide open to suggestions. Seems trains stop running very early. Taxi a good option?, perhaps the train from near our hotel stops early, but some other trains that are reachable by a short taxi ride are avaiable later in the evening to control cost over a taxi. Or do we just bite the bullet, get to the airport by taxi, and take a helicopter?

Key is we do need to get 'home' - ideally before our tour bus loads up and leaves bright and early Wednesday!
The hotel seems well off the beaten path, as I think we will be about 10km out of town;

Servotel Castagniers
1976, Route de Grenoble, RN 202
Castagniers les Moulins 06670
France, French Riviera


Cheers,

Rob
Canada.

So, all went well. We had a great guy on our bus as tour guide, when we arrived in Nice he offered to ensure our bags got to our room later that evening. This allowed us to walk to the train station that afternoon, and taking a very inexpensive train to Monte Carlo (I think it was about 15 euro for the two of us return).

We spent some time walking around Monte Carlo, looking at some of the familiar sights from the Grand Prix circuit, and ultimately we found our way to the casino. Only had one drink each (a wee bit pricy), but was worth it, as my son had just hit European drinking age on the eve of our trip; he still has a bit of a wait for drinking age here in Canada. He had a great time, we spent 15 euros each on the entertainment of throwing money away gambling - he was sensible enough to know we wouldn't win.

Finally we were done what we came to do, and managed to get on the late train back to Nice. We then took a taxi to the hotel for about 70 euro.

All in all with transport, drinks, gambling, and a snack; about 165 euro. Not bad considering it was a good adventure away from our tour group. And apparently they didn't have any fun in Nice.

Cheers.