Shanghai -- some high end and low end recommendations for a US traveler who has never been...
1) Fu 1088 - great fine dining Shanghainese in a renovated old mansion. Reservations are essential and each table is in a private room so there is a minimum charge of $60-70 per person. Be sure to get the red cooked pork, crab roe crostini, smoked pomfret fish, amongst others.
2) Whampoa Garden- also fine dining, set on a location right on the bund. Very refined Shanghainese cuisine.
3) Lost Heaven - Yunnan cuisine. Not super high end, more of a mid range place.
Not sure if you're looking for Western high end cuisine so I've ommitted it here.
Mid range/Low end:
1) Jesse's - this is more of mid range place but it features all the favorite home cooked staple dishes in Shanghai.
2) Jia Jia Tang bao - low end, soup dumplings.
3) Yang's fried dumplings - low end, delicious pan fried dumplings.
4) Ding tai feng - more mid range, in a nicer setting. While its a Shanghai outpost of a Taiwan chain, its reliable, consistent, good service in a clean setting.
Other posts on this topic will come up with the most of the foregoing recs. These are the places I take all visiting friends!