United has round-trip flights from Houston (IAH) to Shanghai (PVG) for $399 with a connection. Flights from mid-March to mid-May. 3-day minimum stay required. No weekend departures. A Tourist Visa is Required for American Citizens.
Note: The Chinese Consulate is in Houston (Montrose), and you can apply and pick up your visa in person. When we did it, it took about 25-minutes, and the turn-around was 3-days.
Note: There is also visa free 72-hour transit, if you plan on only using China as a connection to elsewhere.