The best exit from Shibuya station is the into the Hachikō square named after a dog of the same name. Hachikō was a truly persistent dog born in 1923, who every evening waited outside the station for his master to come home from work. When his master passed away (while at work) the dog continued to come and wait at the station for next nearly 11 years. The dog got so famous, even in its lifetime, that a statue was erected shortly before Hachikō's death.
The famous Hachikō statue above. I think the cover may be due to the winter (it was March) or the spring equinox (a period where one should, among other things, be good to animals). The statue is in the corner of the square.
Just across the square is a Starbucks and Tower Records (as far as I remember), that has 6 or 7 floors of music (CD) and films (DVD and the occasional Blu-ray) and books. Will go back there, always buy a couple of CDs there.
Shibuya 109 (10 means To and 9 means Kyu, a play on words as the store is owned by the Tokyu company) department store, which primarily offers womens clothing. There is an 109-2 which is selling mainly mens clothing. There are also competing stores owned by a number of the large railway companies, another one Seibu can be seen in the background to the left in the picture above.
Good place to get our morning coffee is at Starbucks and a to snap few pictures of the famous crossing, where there is green at the same time for all pedestrians.
If we choose to go to the left of the Starbucks, as seen from the square and then we will end up in a street with small shops and restaurants, but nothing out of the ordinary really. A electronics shop has caught my interest and I have returned there a couple of times and bought a few things.
There are a number of museums and concert places. There is NHK Studio park where we can get a tour of the TV studios. Two large shops, Book 1st, one of the largest bookstores in Tokyo, as well as Tokyo Hands, everything gadget or practical (Home decorations) that is very Japanese (like a rubber duck department) can be found there.
For me a revisit to the music store and Tokyo Hands is a must, I think.
Shibuya's location on Google Earth is here.