car rental

You certainly could do that, but it's much cheaper to just take the train -- about 6€ round trip, if I recall correctly. You don't need a reservation or even a ticket for a particular time -- just board the train you want. It's about 15-20 minutes each way.

If you stick with the idea of driving you will miss all the beautiful views that you get on the train (sit upstairs on the right going to Monaco and on the left returning) and parking in Monaco is either free or quite expensive. Free if you stay less than an hour, quite expensive if you stay 60 minutes or more.

Very little street parking is available, use one of the many multi-storey car parks scattered around the country for the residents.

Be prepared to go up and down quite a lot before the car is parked. The car park near the station for example has over 25 floors - 27, I say from possibly faulty memory.

Much better to take the scenic cheap train, unless there is a reason you want to make things difficult for yourself.

Several (I think 6 from memory) bus routes can take you to the bits that you don't want to walk. They are very cheap, frequent and go everywhere in the tiny country.

Crazy to rent a car between Nice and Monaco. Easy parking is out of the question in Monaco and it is expensive. The train is frequent and cheap.

Train, all the way. https://www.trainline.eu/