definitely newbury street for shops and restaurants. the pru and copley for more high end shopping.
downtown crossing is near the common. it is a t (subway) stop. has H&M among other stores. www.mbta.com has all the info you need for traveling by subway/bus.
two really good japanese restaurants imo are ginza and fugakyu....which are both near the boston univ. campus. they are very close to t stops on the green line on the C line part of the green going outbound.
www.ginzaboston.com
december it gets pretty cold....but i don't think its as severe as midwest weather?
mike's pastry in the north end always gets rave reviews. haven't been there myself (i don't know what i was thinking). www.mikespastry.com
i really hope the weather won't be as bad as it is here. Oooh that fugakyu sounds good..saw really good reviews on it. I just read about Mike's pastry. I guess it is a must to go to. I will definitely check that out, I love pastry. thanks!