Having spent 10 years of holidaying (of the campping kind) on the French Riviera when the kids were young, know it well. Came in off a cruise ship 2 years ago. if you come into Monte carlo itself, not worth booking a trip. You can walk along the front and up to the castle in Monaco in about half an hour, through the gardens, leisurely stroll. Try to get up for the changing of the guards at noon, worth seeing. The view from the fairytale castle is spectacular down over Monte Carlo itself. meander through the little streets opposite the castle (drinks are cheaper the further away you go), pop into the cathedral where Grace and Rainier are buried and near the Jacques Cousteau museum you can catch a trolley bus for a few euros, which will take you down into Monte Carlo, following the route of the grand prix, along the front and past the Casino. It's worth having a leisurely stroll back down to the port and take in some of the yachts.
If you want to get out of Monte Carlo, there is a train line which runs right along the front to Nice within about half an hour. You'll love it, we've done some travelling and it's our most favourite area for beautiful scenery. Now the kids are grown, we still spend a few days there each Summer at a little place called Beaulieu, between Nice and Monte Carlo, set into the Corniche - amazing!
Hope it's of use, let's know if you need any more info
PS while you're over our part of the world, we'll be on a cruise on the Noordam out of New York to the Caribbean!