I have only stayed in Monte Carlo once. I lived near Nice for many years, so often went to Monaco. I went to see the cars, mostly and never failed to see a collection of exotica. Of course I was never last out either.
I agree with keisari unless you have a specific reason to want to stay in Monaco. Hotel prices there are are at least twice as high as in the surrounding areas usually, although there are peak times everywhere on the Riviera.
Commuting by bus or train to Monaco from Nice does not take long and is often entertaining also.
Monaco does have a grotto that people tend to like, and a botanical garden. The real action is the port, castle, casinos, cars and people-watching. Did I say casinos?