I compiled this capsule overview some time ago for a different website, but I believe it's still current and some Chowhounds have reported that they found it useful, so here it is, FWIW:
Shanghai Old Restaurant (Lao Fandian)
242 Fuyou Road
This use to be the lead recommendation in all guidebooks, but the food has gone way downhill. It's pricey by local standards, but mostly only of historical interest. It's the dowdy Grande Dame of Shanghainese restaurants, and there's usually a music ensemble on a small stage playing classical Chinese music. Don't order the braised eel, the last time we were there it was a few meager shreds of eel swimming in an ocean of oil, yet it's one of their priciest dishes. The salt and (Sichuan) pepper ribs are still good, however, and probably the red-cooked pork dishes as well.
Sun Ya (Xinya)
719 Nanjing Lu
I've posted on the importance of this place in the interface between Cantonese food and the western appetite during the concession era and its possible impact on expectations of Cantonese cuisine abroad. Like Lao Fandian, whatever glories its cuisine ever had have faded, and you'll find it very familiar to your experiences in middling Cantonese restaurants in the US. They do (or at least did) have one floor devoted to seafood hot-pot, however, and it was excellent in its bounty of fresh seafood, including live shrimps (the ones that tried to make a break for it got tossed into the pot first). They also serve a great fried milk dessert.
600 Fuzhou Lu
On the surface, Lao Banzhai has some of the similar pretenses to elegance as Lao Fandian (the Eight Treasure tea setups at every place setting is an example) but is in fact less formal, less pricey and has much better food. The braised eel here is very good, and, living up to its reputation as a "Yangzhou style" restaurant, has what may be as good a "Lion's Head" meatball dish as anywhere in town.
22 Lane 1081, Nanjing Xi Lu
Meilongzhen started out as a Sichuan restaurant and morphed into a Shanghainese restaurant with Sichuan characteristics, sort of a spicy third stream alongside the saltiness of Zhejiang cuisine and the sweetness of Jiangsu cuisine. It's one of the toughest tables in town to get, especially during wedding season, and probably the main reason every family's cook has ma la doufu in her/his repertoire. The twice-cooked pork and the eggplant dishes are exceptional. They also have a Sichuan-style tea service, with the long-spout tea kettles.
556 Fuzhou Lu
A favorite of mine, even though it moved from its original homey premises near the old city to a larger, glitzier space. It serves food which tends to be lighter than elsewhere, serving seafood by season and good fowl dishes too. It's especially famous for its herring dishes during winter, but will always have fresh fish and shrimp dishes. It's a good place to try the "squirrel fish", and it also serves a furong chicken dish I like. Along with Meilongzhen, it's the most copied restaurant name from Shanghai
603 Fuzhou Lu
Wang Baohe bills itself as the "king of crabs and ancestor of wine". It's been around for about 250 years, originally as a wine house and is especially famous for it's hairy crab set meals. If you saw the Iron Chef special where Chef Michiba went to Shanghai and prepared a crab feast, it was Wang Baohe's kitchen he took over for an afternoon. Even if it's not "hairy" crab season, they will have plenty of fresh crustaceans available. Pricey, by Shanghai standards, but won't bust your per diem.
255 Dalian Xi Lu (Hongkou)
4. No. 240 Lane, Beijing Xilu
18 Xizang Zhong Lu (newest branch)
Meiyuancun is my wife's favorite for "stepping out" in Shanghai, probably because the original branch is in her old Hongkou neighborhood. Its somewhat unusual in that its fame spread from a neighborhood to downtown instead of vice versa, and there are now two branches in the downtown area. It's strong in the seafood and vegetable areas, and in attention to presentation, but is quite reasonably priced. Meiyuancun also serves what some consider the best Beijing duck in Shanghai.