I just recently returned from Shanghai. There are airport buses that can take you into the city for 20RMB ($2.50). There are 5 bus lines (labled 1-5), but I don't know if you can figure out which line to take. There should be a bus counter at the arrival hall that can assist you. If you are traveling alone (and don't speak chinese), I wouldn't recommand taking a taxi (~150RMB) from the airport. I've heard too many scary stories, but if you are in a group, it should be fine.

The other option is to take the airport bus into the city and then a short taxi ride to the hotel.

Do a search on the web for airport bus and call Westin to find out which airport bus line to take.

Good luck.