Bus nr.200 of Lignes d'Azures runs very frequent (3-4 buses per hour) between Cannes and Nice. The journey takes about 1.5 hours and costs €2 per person (one way). In Cannes you can take the bus at the bus terminal (Gare Routière) at Place B. Cornut Gentille. This is within walking distance from the tender boat station. The bus also makes a stop at Cannes train station before leaving the city. Check the timetable of bus nr.200 before you leave.
Trains between Cannes and Nice run 3 to 4 times per hour. The journey takes about 40 minutes and you pay €6.50 per person (one way, second class). From the train station in Nice, you can walk to the center or you can take tram nr.1 to Place Garibaldi, also in the center. It's worth to check the timetable before you leave. In Nice there are several train stations. In this case select the main station Nice Ville.
How do I get to the train station from the cruise port in Cannes?
Cannes train station is located in the north of the city on Place de l'étoile. From the tender boat station at Quai Croisière it's a pleasant 20 to 30 minutes walk. Walk along the harbor in the direction of Palais de Festivals. Once there turn left and take the Rue des Serbes. This street leads to the train station. If you're in a hurry you can also take a taxi from the port. Expect top pay aroun €10 per taxi (4 persons, one way).