It could be the North End, the MGH area, which is the former West End, or even Beacon Hill. If a reasonable rent, then it would be the "backside" or North facing portion. It could also be one of the apartment buildings around the City Hall area.
The only way to know is to go and look since there are gems and there are tiny hovels in all the places I have mentioned, some in the NorthEnd actually do not have bathrooms, but shared toilets in the hall. There are some cheap apartments on the backsinde of the Hill and just beyond Haymarket that are right next to the T tracks, like five feet away.

Some of the North End apartments overlook the airport tunnel entrances.
Don't want to burst any bubbles....but if it sounds too good to be true....