We recently stayed in Mercure Nice Cap hotel. Five mins walk to beach, has outdoor pool, rooms small but spotless, beautiful bathrooms, tea/coffee facilities, etc.
It certainly doesn't have a sea view, but it's location is great. It is beside the Nice Cap 3000 shopping centre which has great shopping, restaurants, etc.
Also has free airport shuttle bus. Staff very friendly and helpful.
cost per room was approx €85 room per night. Bus in to promenade des Anglais was no more than €2.