I was there many years ago! From what I remember, it's quite small. We stayed in Nice, France and drove there for part of the day. You might want to pick up a book or do some reading about the attractions in Monte Carlo to decide if it's worth it to stay there or travel out beyond Monaco into France.
We stayed there for one night in July - which was sufficient. We stayed at the Hotel de Paris in a Seaview Junior Suite. If $$$ are no issue, then stay in Monaco for a night and be baller - we flew in/out via helicopter, did dinner at Le Louis XV, and gambled at the casino. It was not cheap, but it was a lot of fun. Otherwise, like PPs mentioned, you can stay in Nice and take the train there - I think it's about an hour each way.
There's honestly not a lot to do in Monaco unless you get access to a beach club (which you usually only get through a hotel - or else it costs about 100 Euros/person to get in!), and gawking at the uber-rich people all around. The casino is beautiful inside, but it was not at all the high-roller fun experience my DH was hoping for.
Re: monte carlo monaco
There's honestly not a lot to do in Monaco unless you get access to a beach club (which you usually only get through a hotel - or else it costs about 100 Euros/person to get in!), and gawking at the uber-rich people all around. The casino is beautiful inside, but it was not at all the high-roller fun experience my DH was hoping for.