Do you mean the surrounding hills? There is a walk up Mont Boron that connects to a trail to the Batterie and up to Mont Alban. It can get hot. There is also a nice walk around Cap Ferrat, with less populated coves. There are also a number of beaches where you need to scramble down from the bus or train line. There is also a hike up to the Tete du Chien (you can depart from Monaco/Cap d'Ail or La Turbie) . You can also take a ferry to Ste Marguerite and go hiking and swimming there.
There are also hikes if you take a train or bus. For example, there is the Train des Merveilles that goes to the edge of the Mercantour National park. There are trails that depart from there and from Casterino (a shuttle bus away). This is at elevation and can actually be quite cold, even in August. A few years ago I was absolute frozen up there (with light rain), even though it was 80 and mostly clear back in Nice. Also further afield is the Massif de l"Esterel area (a car might be required for some trailheads).