You can combined Antibes and Cannes in a day (unless you are using it as a beach day) and Eze-Monaco in a day into evening. Menton can be combined with a stop in Villefranche sur mer (or Cap Ferrat/Villa Ephrussi). St. Tropez is tough to get to via public transportation. You can take the ferry or you can take the train to St. Raphael and then a bus. In my view, the highlights of St. Tropez is less the villages than the beach (at Ramatuelle, another shuttle bus or drive), the surrounding villages and rose wineries.
As noted, the LIgne d'Azur is a bus/tram pass that covers major lines in the department (but not the regional lines if you go into the interlands). The train is separate. You want the Pass Sud Azur.. This covers the train, tram and buses, including the regional lines in the Alpes-Martimes (excludes the Var/St. Tropez). 7 days is 50E. There is a megapass that includes attraction admission and discounts called the French Riviera pass, but people often find it difficult to find value there unless you go to one of the attractions listed. In addition, for day trips, you might try a train Day Pass called the Pass Journee][2] (1 department, 20E, 2 departments 35E). The second person on the Day Pass is a 5E supplement. Bus/tram would be separate.