Of course, the Shibuya scramble crossing is a must-see, but if you like art, bunkamura museum is recommended!
They always do interesting exhibitions; the current exhibition is Kuniyoshi & Kunisada, the famous Ukiyo-e painters.
Also, if you want to experience the liveliness, walk along "Center-gai", literally means "the center street". This is a narrow street connected from Shibuya scramble crossings, with lots of restaurants and shops and teenagers walking around. It's a nice way to experience the real Japanese atmosphere!
It may be too typical but seeing "Shibuya scramble crossing" is a must-have experience.
It may seem that Shibuya scramble crossing is easily accessible from Shibuya Station, but it is hard to get there even for Japanese who are not familiar with Shibuya.
Shibuya Station is a huge terminal station with lots of train line crossing. Each gate is in the different areas; some of them are underground, others are on the ground floor, and another on the second floor. It is often said that it's like the last map of the famous video game FinalFantasy.
Anyway head to the Hachiko exit. If you get out from different exits, you might have to walk around so be careful about the exit when you go there. When you're anxious, feel free to ask conductor near you.