What area of Boston are you living in? As for advice, stay away from the Dorchester, Roxbury, Mattapan areas unless you like wandering around rough neighborhoods (or unless that's exactly where you're living >_<). Basically at least one person gets shot there a night and it makes the local news. If you want to go check out stores and whatnot, go to Copley/Prudential, Downtown Crossing, Faneuil Hall, etc. All are accessible by subway (Red Line and Green Line). Try to make it to a Red Sox game, it's a lot of fun even if you aren't a Sox fan. Familiarize yourself with the subway system (namely the two lines I mentioned above) as you can get pretty much anywhere on those lines alone. If I think of anything else I'll post it up And welcome to Boston
Make sure you check out Faneuil Hall like Illuminati said. Great area for shopping. And Cheers (that bar from that really old TV show) is around there somewhere. And make sure you check out some of the college sports, preferably hockey. Unbelievable skill in the Boston area with BC, BU, Harvard, and just a little north you've got University of New Hampshire who are awesome!