The Bund [ 外灘 = WàiTān ] ( map )
Take a river cruise to get a night view of cool waterfront buildings.
Tianzifang [ 田子坊 = TiánZǐFāng ] ( map )
Artsy area by Taikang Road [ 泰康路 = TàiKāngLù ] with trendy galleries, cool boutiques, and hipster cafes in old brick buildings. You can buy all sorts of unique trinkets here. A bit like 798 in Beijing meets hutongs! My favorite area in Shanghai!
Yu Garden [ 豫園 = YùYuán ] ( map )
Walk along Shanghai Old Street [ 上海老街 = ShàngHǎi LǎoJiē ] to the very touristy Yuyuan Garden and have some steamed buns/dumplilngs [ 小笼包 = XiǎoLóngBāo ] as well as sweet or savory sticky rice balls [ 汤圆 = TāngYuán ].
Nanjing Pedestrian Street ( map )
[ 南京路 步行街 = NánJīngLù BùXíngJiē ]
East Nanjing Road [ 南京 东路 = Nánjīng DōngLù ] is a very busy shopping street for pedestrians with nice buildings.
Xintiandi [ 新天地 = XīnTiānDì ] ( map )
Upscale trendy shopping area with pricey restaurants and cafes. Very modern, beautiful area.
Wujiang Road Snack Street ( map )
[ 吳江路 小吃街 = WúJiāngLù XiǎoChīJiē ]
A street selling a wide variety of eat in or take out food. Particularly busy at night.
Qibao Ancient Town [ 七宝 = QīBǎo ] ( map )
Seven Treasures Old Town is area with buildings done in the old style, selling lots of local food and snacks. If you don't have time to go to an actual ancient water town, this might satisfy your itinerary.
Shanghai Ocean Aquarium ( map )
[ 上海 海洋 水族馆 = ShàngHǎi HǎiYáng ShuǐZúGuǎn ] official site
9 am – 6 pm  |  160 RMB
Yes, the underwater tunnel is quite long. However, the aquarium was extremely crowded when I went, with people repeatedly tapping on the glass and speaking very loudly (as you can hear in the video). If you're looking for a tranquil day at an aquarium, this is not the place, unless you don't mind being constantly surround by obnoxious people harassing the marine life.
Longhua Temple [ 龙华寺 = LóngHúaSì ] ( map )
Quite a nice temple that's surprisingly quiet. Easy access via metro and also near a TESCO supermarket
People's Square ( map )
[ 人民 广场 = RénMín GuǎngChǎng ]
Basically a nice park in the city with lotus ponds and people hanging out playing chess.
Jingan Temple [ 静安寺 = Jìng'ānSì ] ( map )
Just a temple within the city... wouldn't say it's a must-see, unless you've never seen a temple before.