The main district, Monte Carlo, personifies opulence with its fancy casinos, including the lavish Grand Casino, and multi-million dollars yachts docked in the harbor. A feast for the eyes!
The lavish Grand Casino is very luxurious and a delight for the eyes but be aware that it will cost you 10 Euros to visit the Salle Renaissance, the Salle Europe and the Salle des Amériques and an additional 10 Euros to if you want to go see the Salle Blanche, the Salle Médecin and the Salons Super Privé. Also, a dress code is enforced: no shorts, sneakers or flip-flops.
The splendid Palais du Prince is open to the public during the summer months, however it will be closed if the prince is there. You will be able to tell, as they fly the state flag in the presence of government officials.
Monaco also hosts the Grand Prix (Formula 1) race late May and would be extremely crowded. Just think about those speeding racecars when you see the narrow streets to gain a real appreciation for the skills of the drivers.
The Oceanographic Museum, perched on the side of the cliffs, will most certainly delight all ocean enthusiasts.