I find good Shanghai dumplings (aka xiao long bao, soup dumplings or XLB) at Shanghai Cafe on Mott Street in Chinatown. Joe's Shanghai is decent, but not in Shanghai Cafe's class.
I'm afraid I haven't come across anything at Shanghai Cafe level in Boston, but in contrast to multiple people in this thread, I'd place Wing's Kitchen in Chinatown and Shanghai Gate in Allston above Taiwan Cafe (which places third). Haven't been to New Shanghai yet, and I have regretted trying them anywhere else in the Boston area.
23 Hudson St, Boston, MA 02111
204 Harvard Ave, Allston, MA 02134
100 Mott St, New York, NY 10013