How to get from Monaco to Nice by public transport? [duplicate]

You'll want to see the post @Karlson linked to in his comment for all about how to get from Nice to Monaco/Monte Carlo by bus or see sncf for a train connection.

In order to travel onwards to Venice you might look at going by train - since all the high speed trains seem to have been abolished on the eastwards leg from Monaco you'll have to go to Ventimiglia by the local train from Monaco and from there to either Milan or Genoa with local trains - and onwards with the Frecce (Italian high speed trains) or even making your way with InterCity trains which can be much cheaper, but tend to be also much slower - see trenitalia.com.

For Venice you'll find there's two train stations, one in Mestre which is on the Italian main land and you'll have to get on a shuttle train to cross the bridge to Venice itself, the other one is Santa Lucia which is just on the other side of the bridge.

Note: in Italy it is well worth buying train tickets ahead of time for all trains apart from local trains to get some fairly healthy discounts in many cases.