What are your interests? Why did you choose Japan? Have you travelled much before? What kind of budget do you have? Have you done any research here (or elsewhere?) There are a lot of threads already about this/places to visit. Many people do a "greatest hits" of Japan, others use their interests (food, cycling, hiking, photography, etc) to help plan their trips. Without knowing anything about you and your friend it's hard to give any specific useful advice.
Most people who come to Japan do the standard Tokyo-Kyoto-Hiroshima route, with small variations in between. If it's your first time in Japan and you're not sure you will ever come back, it's a good place to start. I would definitely consider Tokyo and Kyoto as base cities, which would allow you to do day trips from each, although some places are even better overnight. Both Tokyo and Kyoto are worth at least 3 days each, although you could spend a lot longer in both. In both cases, be aware that sites are spread out in different areas of the city, so whatever you plan, plan by neighbourhood, so you don't waste time travelling from one end of the city to the other.
Osaka gets a bad rap on this forum, but it's well-loved by many Japanese. If you are into food, nightlife, shopping, etc. it would be a fun place to stop, although Tokyo has all that and more. However, unless there is something specific you want to do there, I would probably devote my "big city" time to Tokyo rather than Osaka, and plan more time elsewhere. OTOH, if you don't plan to go to Tokyo, then you can get your big city fill in Osaka/Kobe.