Go to visit Monte Carlo in Monaco; a short bus or train ride away. You can see the residence although not open for visits until June but they have a very nice changing of the guard at 1130 each day,etc. The town is interesting to visit as is the world famous casino and aquarium.......
Another 20 minute ride to Menton which is much like Italy and the last stop before reaching the border; it is a very colorful and interesting coastal city....
Too bad about your distaste for art; great Chagall musueum in Nice as I recall and a ten minute bus ride away is Antibe with the Picasso musueum--he live nearby and painted a lot of this area.
The visit to Eze is very nice; the walk up to the top, the views and if you are the educated person you seem to be, well this is where Nietzsche wrote the last section of Also Sprach Zarathustra....there is a well marked trail that he walked and pondered this now classic work.
Old town Nice itself is a nice place to just walk around.....
I will say that the beach at Nice is a far far cry from the one at Corpus Christi....I have spent a lot of time on each............
I would also add that art history in school is not the same as viewing masterpieces in person. I too took a lot of art history in school including a few courses for a master degree requirement and I have not to be not enthralled by the unique museums that dot the countryside of the south of France.......