Hello, I am wondering the best way to get from the North Railway staion to the hotel- Garden Hotel Suzhou

At the north railway station, you may find bus 811 to reach Wangshiyuan Station. Get off the bus at Wangshiyuan Station. Then you can walk along Daichengqiao Road to your hotel.
From your hotel to Dushu Lake, there is no direct bus, so it is suggested to take a taxi to reach there diretly. There is about 10 to 11km from your hotel to that lake.