Though this list is not exhaustive by any means, here is a collection of few places in Shanghai that I think are popular among foreigners:
新天地 (Xīntiāndì): Xintiandi
新 (xīn): new
天 (tiān): sky; heaven
地 (dì): land; earth
天地 (tiāndì): heaven and earth; world
Xintiandi, which literally translates to New World, is an area in Shanghai full of expensive restaurants, bars, cafes and galleries. Even though it might not feel like China, this place is popular among Chinese people and foreigners alike. If you go there, expect to spend some money (or you can always go there and just look around).
外滩 (wàitān): The Bund
滩 (tān): beach
The Bund, known as wàitān in Chinese, is an area along the western bank of Huangpu River. While this area consists of numerous historical buildings, it is also equally popular for the view of Pudong on the opposite side of the river.
South Bund Soft-Spinning Material Market, also known as the Fabric Market, is another popular place for foreigners to visit in Shanghai. Here you can find custom made clothes in the cheapest price possible. Just to give you an idea, you can get a custom made suit for under $50.
七浦路(Qīpǔ lù): Qipu Lu
Qipu Lu is popular among the foreigners as the place to go get cheap, knock-off stuff. I used to call it Cheap-u Lu. If you decide to go, make sure you bring some bargaining skills with you.
路 (lù): road
路 means road, so its English name would be Qipu road. In some cities you might also find that 街 (jiē) is used instead, which means street.
街 (jiē): street