[Nagoyankee]

The fastest way would be :

Ikebukuro > Yoyogi by JR Yamanote line (takes about 10 minutes)

Yoyogi > Roppongi by Subway To-ei Ohedo line (takes 7 minutes)

Tokyo is a very safe city in general. I've lived in central Tokyo for over 20 years and I'm still in one piece. But if you're female, you might want to avoid walking around Roppongi alone after around 12 midnight. That's where a lot of foreign residents, tourists and the U.S. soldiers go to drink. So it CAN get pretty wild at times.