Yes, you can visit all these places by subway. Most of the bullet trains from Hangzhou to Shanghai is arriving in Shanghai Hongqiao Railway Station. I checked on the China train page https://www.travelchinaguide.com/china-trains/ and only find two high speed trains that will arriving in Shanghai Railway Station. You known the Hongqiao Railway Station is a bit far from the downtown area, but metro line 2 can take you from Hongqiao to Nanjing East Road Station for the Bund area and Lujiazui Station for the TV Tower. Yuyuan can be reached by metro line 10, only one stop from Nanjing East Road.