There are others who have replied who are more expert on the area than I but your plan looks good to me. Glad you picked the Breakers as the mansion to visit. I've been there twice and it never ceases to thrill. Second choice to me would be Marble House but I frankly think one mansion a day is enough. They are quite overwhelming. Good idea to take your own refreshments. There are none along the Cliff Walk. We found the Japanese Tea House closed when we were there. No restrooms either on that walk.
Speaking of Marble House it was built by one of the Vanderbilts as a gift to his wife who then divorced him and moved down the street to Belcourt, another mansion. Someone else noted Rosecliff as a favorite. I really like its exterior. In the old days we'd say take plenty of film!