The suitable clothing is required. In the private rooms after 22.00 a jacket and a tie must be dressed. There are a few cafes in “Grand Casino” and around it. This portion of the casino definitely does not have a dress code. The slot machine area of the casino requires no formal dressing but the main area does.
Also many of the popular bars and restaurants like the American bar in the hotel de Paris require you to wear a coat and tie. So I suggest you take some formal clothes. I guess it depends on whether you want to go inside and look at the high rollers.
Look at it this way, it’s never a waste of time to pack a jacket and tie for Monte Carlo, it’s such a glamorous location it’s a shame not to dress up. Most people do, you’ll find the young playboys who go for cocktails to Sass Cafe and then on for dancing in Jimmyz wear blazers over their designer shirts and jeans. Enjoy and don’t forget the credit card.