Tokyo is too large to see comprehensively in three days, so this itinerary picks one dominant neighborhood per day — traditional Asakusa, central Shibuya and Harajuku, then a mix of gardens and modern Tokyo — rather than trying to crisscross the whole city.
Start at Senso-ji Temple in Asakusa, Tokyo's oldest and most atmospheric temple, and browse the approach street for souvenirs and street food. Head to Tokyo Skytree nearby for city views, then cross town to the Imperial Palace grounds in the afternoon. In the evening, a Tsukiji Outer Market Food Tour is a good way to sample Tokyo's food scene in one go.
Cross the famous scramble at Shibuya, then walk to Harajuku & Omotesando for its mix of youth fashion streets and upscale boutiques. Visit Meiji Shrine, tucked into a forest right next to the district's chaos, and end the afternoon at Shinjuku for its skyscraper views and neon streets after dark.
Spend the morning at Shinjuku Gyoen National Garden or Ueno Park, both a calm contrast to the city's density. In the afternoon, choose between teamLab Borderless for its immersive digital art or Akihabara for anime, games and electronics. If you have a fourth day, Mount Fuji & Hakone is the classic day trip out of the city.