In Monte Carlo, just outside the rail station upstairs, there is a Hop On Hop Off bus, cost 3.60 euros each. Can't remebmer the color of the route we did, but it went up by the Castle. Changing of the Guard is at 11:55 daily.
There is also a 30 min Tourist Trolly you can board near the Castle. There are headphones with recordings in 12 languages. It was about 7 Euros in Oct.
Our ship was anchored at Villefranche, and the train was 18-20 minutes.
If you take the train from Monaco back to Villefranche, and the tell you Platform C, you have to walk way down the platform, as it doesn't stop that close to the walkway from the terminal. We almost didn't get the train back to Villefranche.
Casinos don't open until mid-afternoon. You need a passport to go in, and Formal attire to go into the main casino. There are apparently some slot machines in the lobby, but we didn't go in.
Architecture was interesting. Didn't have enough time to do much.
One warning -- there is a restroom in the back of the block of shops by the Castle, but you have to pay to pee. A lady takes your money and gives you a few sheets of toilet paper.
Have fun!