If you insist on the combination of cocktails and Asian food, the closest (but not necessarily the best) place is probably the P.F. Chang's in the Cambridgeside Galleria. They have an Asian Pear Mojito and some other interesting Asian-influenced drinks.
Venture a little further away . . . to Brookline, for example. . . and you can get some of Boston's best sushi along with a fine selection of sake and cocktails.