1. Shibuya CrossingShibuya Crossing is the busiest pedestrian crossing in the world. Its bright lights and billboards are stunning.
2. Harajuku / Yoyogi ParkHarajuku and nearby Yoyogi Park are popular gathering places for (many of) Tokyo's youth subcultures. It's a good spot to get shots of Japanese street fashion.
3. ShinjukuShinjuku is a massive neighborhood that would be a metropolis on it's own (without the rest of Tokyo). It's urban exploring at it's best.
Be aware: people in the Kabukicho area of Shinjuku often don't like to have their photo taken. Kabukicho is a fairly dangerous area.
4. GinzaGinza is Asia's premier upscale shopping neighborhood. It has interesting architectural features.
5. OmotesandoOmotesando is another upscale shopping district that's full of interesting architecture and fashionable people.
6. OdaibaOdaiba is a good spot to get photos of Tokyo Bay and Tokyo's skyline.
7. Aoyama CemeteryAoyama Cemetery is Tokyo's oldest cemetery. It's a massive park-like Japanese (and Western) cemetery. The contrast of the natural setting and the massive buildings of Roppongi in the background is interesting.
8. Tokyo Sky TreeTokyo Sky Tree is the second tallest structure in the world. It affords the best views of Tokyo from above.
9. Hamarikyu GardensHamarikyu Gardens is a large Edo-era Japanese garden located beside Shiodome (one of Tokyo's largest business districts). It's a popular spot amongst local photographers.
10. YurakuchoYurakucho is an old part of Tokyo that hasn't changed much for the last 70 years. Check out the tiny Izakaya under the railway tracks. It's Tokyo nightlife at its best.