I am coming to hangzhou at 14th dec. 2013. i want to visit the city in two whole days, what are the most important sites and convenient way to visit around city by myself.

Hi, you cannot miss West Lake Scenic Area, Xixi National Wetland Park and Qinghefang Ancient Street.

If you stay near the Yuquan Campus of the university, you can easily walk to the West Lake. To Xixi Natioanl Wetland Park, you can walk from the campus to Gudang (west of Wantang Road) bus stop to take bus no. 83 or 356 to reach.
To Qinghefang Street, you can take bus no. 28 at Zheda bus stop to Wulin Square South and then transfer to local subway line 1 to Ding'an Road, which is within walking distance from the street.

If you are interested, I also recommend Thousand Island Lake Scenic Area to you. You can take a direct bus to get there at local West Bus Station.