Some neighborhoods don't have sharp boundaries and just sort of mush together.  (That's "mUsh" not "mEsh".)  Here's a map, of sorts.  For example, some people refer to a part of Back Bay as the Copley Square area.  NOT on this map is "Financial District" which is also convenient and called "Downtown" on this map.  As you can see, Back Bay is right next to the Theater District which then melds into Chinatown.  I have no idea what the "official boundary" is between BB and TD; Charles St, maybe?  Who can tell

A couple of things for foreigners to listen for quite carefully.  On the map (posted below), there is an area called the South End.  The South End is NOT South Boston aka Southie, so don't confuse those two very different areas of the city.  There is a "Roxbury" (not labeled, just on the edge of the map) and a "West Roxbury"; do not get them confused. Talk about "and never the twain shall meet"!  On the map is the South End and the North End (Boston's Little Italy); there is also a West End (it's kind of between Beacon Hill and North End on the map).  There's an East BOSTON but I don't know of an East END.  

Bring a map and your sense of humor and if people look at you funny for saying the wrong thing, don't worry about it

Re: Thanks for the info!

Both are in the city. Back Bay is MUCH nicer though. The Theater District gets a little sketchier at night but not terrible. Back Bay is definitely nice though.