Basically, Beijing is a must.

Great wall,palace,etc. One week is long enough even for bars/music, art store, Museum.

Then you need to talk to your friend, like what did he/she know about china.

If me, i prefer to Shanghai/Hangzhou/Suzhou/Zhejiang old towns, are all very good for the scienes/culture. and it is more conveneint for lodges.

The reasons are:

BJ,SH are famous, they can talk to their friend after they come back.

It is good to arrange lodge/air ticket stuff. For Shanghai, it is good for shopping. And it is close to Hangzhou/suzou, which are the heavens.

All those are modern cities, they will have a good impression for china. Somehow, it is even better than most western cities for night life, like foods,bars,entertainment.

Xi'an is also a good choice. If they want to see Bin Ma Yong,etc.

Other places are not good for 2 week plan.

Of course, it depends. If he want to run like crazy, he can stroll here and there without stop.

But if he/she want to enjoy, i guess BJ and SH is good enough.