We are celebrating a milestone anniversary and have 3 days in Nice. I would love to maximize and make the most use of our time there. I'd like to spend a day exploring Nice, on the day of arrival. And then would love to do a day trip. What would be good towns to visit in one day in addition to Eze? We are New Yorkers so expect to be walking a bit. We also enjoy good food (good local cuisine,please). My husband enjoys all things historical while I enjoy both historical ruins as well as various art museums. Would a guided tour be the best way to get around? Is a trip to Montecarlo worth it? Is there much to see beyond beautiful casinos? Lastly, is day trip to Antibes worth a trek?