I agree with Moondog's advice about trimming itinerary to spend more time in Beijing, but that is strictly a personal bias. I never tire of Beijing.

Xian's clay army is stupendous but the city can be gridlocked and a bit of an eyesore; you can see the terra-cotta army on a day trip, if time gets short.

Guilin has also become very touristy, though the karst scenery is awesome; i'd catch an early morning boat down the Li River, rather than lingering in Guilin.

Shanghai is the most Westernized city and sheer numbers of people can be overpowering, but it used to have wonderful - and genuine - antiques, if you are interested in that.

Weather: I've seen snow in Beijing end of March, start of April, but later in the month should be quite nice and warmer, of course, in the south.