6 days Shanghai and Beijing
I would like to visit Shanghai and Beijing from Hangzhou some time next year. Would 6 days be enough for the whole trip. What would be the best time to visit these places and will someone kind enough to provide some tips to places of interest and the mode of transport to go around.

6 days is OK.
D1 Hangzhou-Shanghai
2 hours train, tour Nanjing Road, The Bund, Yu Garden, Yu market, watch Shanghai Acrobats Show at night.
D2 Shanghai
Jade Buddha Temple, Shanghai Museum, Oriental Pearl Tower.
D3 Shanghai to Beijing
Free time shopping in Shanghai. Fly to Beijing
D4 Beijing
Forbidden city, TianAnMen Square, Temple of heaven, watch Beijing Opera at night.
D5 Beijing
Great Wall tour and Ming tombs
D6 Beijing
Summer Palace and Hutong tours.
Enough time? From beijingholidays.net, I read some articlets and copy some itineries. Hope it can help you. You might even take ‘Z’ serials overnight train Shanghai to Beijing, to save one night accommodation.