After a wet start to late spring/summer be prepared for some high temps when you arrive. Please note when driving in France there are notable differences in laws and a much lower limit for drunk driving. The corniches are going to be packed this time of year.
After you visit Eze, continue up to La Turbie and see the Trophee des Alpes. You can also see the Tete du Chien. Both lookouts will give you views with fewer tourists than in Eze. You can stop in VilleFranche-sur-Mer and then go to the Villa Ephrussi on Cap Ferrat. Don't bother driving around unless you like looking at walls, fences and hedges. The walk around Cap Ferrat is the scenic thing to do.
Instead of Grasse consider instead Tourettes-sur-Loup, Gourdon and a loop through St. Paul de Vence. Might be too much in a day combined with Cannes and Antibes. Gourdon is tiny but has the effect of a hilltop castle. There is a lovely monestary and tower on St. Honorat island (from Cannes) and a big Fort in Antibes (and near VSM)
The Luberon valley will be finished/harvested with Lavander at this point. You need to go to higher elevations, like in Sault, but that is a pretty long day trip away. If you do go to the Luberon, the village of Lacoste has the Cardin castle at the top. There are some fields in the Var but the Corso des Lavandes is finishing up as the harvest wraps up.
Parking: It can be difficult to find parking in VilleFranche-sur-Mer as the city is blocked off during peak days. The lot at the Villa Ephrussi is pretty small. The most popular lots in Nice are often taken, so arrive early and consider taking the trams to get around versus searching for a parking lot.