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The Cruise companies block book seats on certain flying routes, which enables them to negotiate cheaper seats. Sometimes one is lucky if they fly you direct or in your case not so lucky, which involves a coach journey. It depends on the best deal they get from one of the many flight operators that are available. When we cruised out of Genoa a couples years ago, we arranged our own flights, flying the previous day, stayed at a hotel and although we had to pay for our transfers, we were still a few £'s in compared to what MSC wanted to charge us. Regarding Day rooms, you should ask your TA or MSC, if you booked the holiday direct with them.
Most cruise operators do this to ensure that if there are any delays you will still catch your plane. As you are a large group you could check the internet for private hire companies offering bespoke trips around Nice but you do need to consider if there is really enough time. The problem that we encountered is that often the cruise companies have a block booking and seats are not allocated until check-in. It is likely that half the plane will be occupied by MSC customers, most of which will have been waiting patiently in the departure lounge for 4-5 hours. If you leave checking in until the last minute you are likely to find your party spread around the aircraft in an assortmernt of single seats.
120 mile transfer by coach is kinda taking the mickey, but there are limited flight options for Genoa. ......... get seats on the right-hand side of the coach for some spectacular coastal scenery. .............. for the return you have 5 hours or more to spare, yes I'd be inclined to sort out a private tour/transfer - with a party of 4 or more it's gotta be cheaper than cruise line's offerings, as well as more flexible since ship's tour has to allow for a range of flight times. ....Or locate a left-luggage facility. .... you don't mention your disembarkation port or airport ................ Chris.
I have done this transfer with MSC, about 2.5 hours, a very picturesque route along the coast road, but the drivers will not stop so make sure everyone is toileted, fed and watered before you leave Nice. If a number of coaches all turn up at the port at the same time expect to be held in your seat for a further period of time.........Wilba.