You can get the train from Cannes to Monaco very cheaply, a journey of about 30 miles.
You can get to Rome cheaply by train and October is a good time to visit as it isn't too hot. This question has been raised many times so if you type rome into the keywords box of 'Find a Question (highlighted in blue) on this site you will find previous replies. I've just had a look and the 7 replies to johnson of Grimsby on 17th July should help you. For train times go to www.trenitalia.com and select the english option top right. Get the earliest train possible and get an early train back to allow for cancellations (don't forget the ship won't wait for you). Important : you must validate your train tickets before boarding the train - insert into yellow machine on platform - otherwise you could get a hefty fine!!!
I will be on the OV2 from 14th Oct, and was also looking forward to Monte Carlo.
I have checked with SNCF and a return rail ticket from Cannne to Monte Carlo is about £14 - not a bad fare I think - maybe it's worth a look!