Wow, ten days are enough for you to enjoy the beautiful Shanghai landscape. Beside shopping, you can spend more time to visit the famous Shanghai attractions(https://www.travelchinaguide.com/attraction/shanghai/) , such as The Bund & Huangpu River, Jade Buddha Temple, Yuyuan Garden and Oriental Pearl TV Tower. If you have time, you can also have a side trip to the nearby cities, such as Hangzhou, Suzhou and Nanjing. See Shanghai Tours(https://www.travelchinaguide.com/package/shanghai.htm) , I think it is helpful to you. I used to find various wonderful travel tours in China Tours(https://www.travelchinaguide.com/tour/default.htm) , if you have interest and more time, you could refer to it to visit the beautiful China. Anyhow, wish you a good time in China.
Ttravel between Shanghai and the nearby cities, you may try the high speed train. It is comfortable and saves a lot of time.
Since you live in Peace Hotel, you can take the maglev from the airport to Longyang Road, then take subway line 2 to Nanjing East Road to your hotel.