I am planning to go there with my mum.
Any advice?

1/2 day at most and many here will say don't go. I liked it - kind of a novelty and the Grand Casino was nice as were the glitzy yachts in the port - otherwise not much to longer. take trains there and up and down the Riviera from StRafael to Italian border and beyond. For lots on trains check www.oui.sncf; BETS-European Rail Experts and www.ricksteves.com.

You can make a neat day by taking a bus from Monaco to Eze, a nice village with stupendous views over coast and also sells lots of perfumes.

Either don't bother or spend a half-day there.

If you're coming by yacht you can fill a few days, I suppose.

Half a day is plenty. It's not a must see, but it's not a waste of time, either.

The question seems a bit strange since you are currently in the area (or at least were last week) experiencing bad weather in Nice.

Well she's probably still there - how do you know they are not? Anyway it's a question that many may be interested in.