-Prince Rainer's palace. Not much to do. It is similiar to many other European palaces and has a changing of the guard around 11:30 daily. I found it boring. Certainly NOT Buckingham Palace.
-Casino. The grand Casino that is famous charges to enter and has a dress code. We skipped that. A plebian casino has opened nearby, but doesn't have the same history or aura.
-Thermes Marins. This is a spa/health club that is attached to the two most expensive hotels in Monaco. We were encouraged to get some 'treatments' which included a back massage, whirlpool/jacuzzi, 'underwater shower', and an algae wrap. The cost was 770FF per person, but really worth it. My wife and I lounged around in white terry cloth robes and swam in a heated pool full of Medditerean Sea water that was pumped from the bay. Marvelous experience and the only reason I would return to Monaco.
Quick Tips:
The SNCF runs through Monaco. The only stop is in Monte Carlo and the train station is built into the side of a mountain so you can exit through 2 different tunnels depending on if you want to go to the casino or palace.
Unless you've never seen a changing of the guard or the inside of a casino or palace, skip Monaco. It is incredibly expensive and the sites aren't worth the time and money. It is the playground of the world's rich and famous, but you probably won't see anybody. Unless it is on your 'must see' list, skip Monte Carlo
Best Way To Get Around:
Walking is the quickest. A bus system does run through Monaco, but it stops frequently and the traffic is horrible! Walk and enjoy the sea breeze, view and people watching.
Absolutely DO NOT DRIVE in Monte Carlo. It only has one main road and is filled with tour buses, citizens, and tourists. Take the SNCF from neighboring Nice or Italy.