I've been to Mougins. It's a lovely town with beautiful lanes and small galleries/studios, and some very good restaurants. If you have a specific reason for being there, then by all means make the effort. If you are staying in Nice for four days, I'd focus on places like St. Paul de Vence (similar, more crowded at peak times but the surrounding countryside is nicer and the Fondation Maeght is there) and if you have a car, a venture on to Vence, Tourettes-sur-Loup and Gourdon. You can even hit Mougins in a grand circle route with some of the other towns near Cannes. But you may want to prioritize some different places like Eze, Menton, Antibes, or some of the other smaller towns if your time is limited, especially those closer to the sea.