Viewing Tokyo skyline at luxury bars is my best plan. Some of my recommendation is "Peter" in Penninsula Tokyo, "New York Bar" in Park Hyatt Tokyo. Especially at New York Bar, they play live jazz music which adds romantic mood.
Roping Hills fulfills your day with various places. They have a cinema complex, beautiful traditional Japanese park called "Mori koen", shoppings malls, high observation deck can see entire Tokyo, restaurants and cafe.
Tokyo is filled with attractions and I am sure there are answers to all your interests.
If you like nature and park, Ueno Park and Shinjuku Gyoen is the largest park in central Tokyo. Rikugien in Komagome (a northern station in Yamanote Line) is a nice Japanese garden. Autumn colors of leaves and sakura cherry blossoms are especially famous.