Another Shibuya location is Shabu Zen, the restaurant where Bob and Charlotte have their first tense moments. It's located in the basement of the Creston Hotel and offers tasty serves of shabu-shabu and sukiyaki. Prices are reasonable, particularly the lunch specials available during the week.
Bob and Charlotte are often pictured roaming Shinjuku. The neon-saturated street that Bob sees from the window of his taxi at the beginning of the film is the Kabuki-cho side of Yasukuni Dori. Charlotte visits a pleasant, but not particularly special, temple called Jugan-ji (walk south from Nakano Sakaue station on the Maranouchi line to find it). And the mysterious whisper-in-the-ear farewell scene was filmed on two streets Plaza Dori, near Shinjuku post office, and Chuo Dori, which connects to it.
Finally, there's one place in the film that doesn't exist the raunchy strip club scene was actually filmed in a fashion boutique in Harajuku called APC underground. The strippers were recruited from real clubs in Roppongi though, so if you're desperate to see naked dancing ladies, head there.