The highlights of Tokyo include, The Imperial Palace, Meiji Shrine; Asakusa district famous for Sensoji temple and Nakamise shopping street with cheap, antique kimonos, geisha bags and beautiful paper products, Sensoji temple, and the Kappabashi kitchen street for those plastic replicas of food seen in restaurant windows. Ueno for its park and museums, Akihabara for electronics, Shinjuku for its shopping with its huge Takashimaya department store and food hall, Tokyu Hands eight level craft store and Uniqlo store for really cheap, high quality, basic clothing, Harajuku for cheap shopping and Japanese street fashion, and Shiodome for entertainment.
Other places of interest include Shibuya for its famous intersection where the style tribes gather and Shibuya 109 the 10 level fashion emporium. Roppongi traditionally known for its nightclubs and bars, but now for its numerous upscale boutiques, smart cafes and Roppongi Hills with the 52 storey Mori building and Tokyo City View a walkway that wraps around the building offering 360 degree views stretching as far as Mt Fuji. Ginza for Matsuya department store and food hall.
At night time Tokyo really comes alive with mazes of blazing neon lights, tiny street stalls, bars complete with karaoke boxes, and the amazing pub food of yakitori and izakaya.
I recommend using the JR Train Line (Yamanote loop line) to get around Tokyo and explore the small cities. There are also lots of budget hotels to stay at all around Tokyo. Try a Business Hotel for a good compromise with prices around $70 for a single room and $100 for a double. Capsule Hotels are also found in most large hubs and cost around $40-$50 including access to the hot baths and sauna. I highly recommend trying these at least once for the fantastic experience.
I also love Yokohama which is just outside of Tokyo for its atmosphere. It was like a smaller version of Tokyo without all the hustle & bustle. Try the world famous China Town in Yokohama for great food and the bay area for entertainment.
These are some great resources to help you explore Tokyo