Hi Marc, the most cost effective, though with 4 cases it could be 'interesting' is the number 110 bus from the airport into Monaco. However if you look at the attached link you will note there are some 12 or so stops, so you will need to know in advance which stop would be best for you.
Also the bus is unlikely to stop unless the driver is aware that someone wants to get off, so check for push button ringers, and watch the bus stop names.
There is also a train not far from the airport, but I couldn't find it's correct name, it is not just Nice.
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