There've been a few Boston-oriented threads here already -- searching Google for Boston, limited to this domain, should give you summaries of the threads that you can pick and choose from.
My memories aren't getting any more recent, but you're living in one of the best cheap-eats 'hoods in the Boston area, and between the Red line and the buses that go through Central Square, you've got a lot more options. Inman Square isn't far away, although it's gotten a bit more upscale since I moved. East Cambridge (down Cambridge St. from Inman) still has some Portuguese spots last time I went through last year, although it looks like the Polish part of the neighborhood's been gentrified away.
Harvard Square still has some good spots (look for Darwin's, on Mt. Auburn a few blocks outside the Square proper, for some fantastic sandwiches -- last Christmas I made a special trip there and it was as good as I remembered). At the other end of Harvard is Bartley's, decent burger joint. (And in between, if I remember, is Stuff-It, which has been doing wraps for some 20, 25 years, and is still one of my favorite options in the Square. A guilty pleasure that actually isn't that unhealthy...)
I don't really remember much being in Porter Square, but around Davis Square there are a few spots worth checking out -- if the Someday Cafe is still there, it was one of the reasons I moved to that neighborhood, along with the Rosebud, a restored Pullman diner. (The food isn't spectacular at the Rosebud, but hey, Pullman diner.) Mike's has decent pizza, not great -- for great, I always ordered from Santoro's (actually around the corner from the Rosebud). (For barbecue, ignore Davis Square's Redbones and get your barbecue from Blue Ribbon on Mass. Ave. in Arlington. Much better, although seating's pretty limited.) Down the street from Davis Square, Teele Square has some great cheap eats, including my favorite cheese steak subs at Angelina's.
Incidentally, to the extent you may or may not cook at home, Davis Square has two greengrocers and a good butcher. I think there's still a bakery there as well, although the star, Carberry's, moved to Arlington.
In Chinatown, I liked Ho Yuen Ting (although there were two or three locations and they varied wildly; I liked the one that's in a basement), the Golden Gate for very good Chinese-American (I liked their pan-fried noodles something fierce), and King Fung Garden is scary good considering its context (a former gas station building), with a large selection of homemade dumplings. I'm given to understand it's a favored spot with both chefs on their nights off and MIT's substantial Chinese community.
For Italian, you may as well go to the North End -- there are other places all over the Boston area, but why bother. (But keep in mind the North End has its tourist orientation. I can't really help; the crowds in the North End made it unappealing to me.) The exception would be East Boston, but I understand the Italian community there has moved along and been replaced predominantly by Asian immigrants, mostly Korean and Vietnamese I'm told. There used to be a lot of great sub shops in particular around there, but I can't promise much now beyond that it might be worth asking about.
Something worth considering is that Boston takes its ice cream far more seriously than Chicago does -- Toscanini's is the standard, but Rancatore's is the well-kept secret where I'd go to talk ice cream with ice cream lovers. And Herrell's in Harvard Square is a pretty serious spot too. There are a few other options, such as JP Licks; as long as you avoid the national chains, you should be fine, and it's well worth finding out what each outlet does best.
Oh, come to think of it, heading west from Central Square over the river, take Western Ave. through Brighton into Watertown, where it becomes Arsenal St. Just past the malls on the right -- across the street from the former arsenal -- should be a brick building that was one of my favorite diners back in the day.
Another area worth exploring is Kenmore Square, which is very close to Boston University -- great diverse neighborhood that should provide lots of options (along with plenty of scalpers whose Red Sox tickets may possibly be real; if you aren't into crowds, don't go to Kenmore on game days). Beyond that, Northeastern University and the medical district beyond it usually have a bunch of pretty good lunch trucks, again a pretty diverse area. Oh, and Brookline Village (Green Line or the 1 bus from Harvard Square) is no longer particularly cheap, I hear, but you can finally enjoy some real pastrami out there.
As a rule of thumb, incidentally, avoid any sub shop or pizza parlor with "House of" in its name. It's not a chain, and I have no idea why there are so many unrelated places with variations of that name, but they really are universally awful.
Good luck -- have fun and report back if you can.