Visiting your beautiful city soon and would love some input about the neighborhoods.  It seems like the area is divided up quite a bit into small neighborhoods - Quincy Market, Boston Commons, Waterfront, Copley Square, Cambridge, South Boston, Harvard area, the Airport area and then the suburbs like Wakefield, Burlington/Lexington, Newton, Randolph, etc.  

Wikivoyage Boston has a reasonable grouping of neighborhoods and should get you started on the basics.
The nicest parts are Back Bay (new-ish money), Beacon Hill (older money) and Downtown (tourists), basically.

For your first trip, I'd recommend the Back Bay or the Theater District.  These areas are right next to each other and have businesses and a big shopping mall and as such there are people day and night and there are restaurants and activities.  Just avoid the Midtown hotel.

Being in Boston proper is the most pedestrian friendly HOWEVER the subway-train will get you around very easily.   I've only tested waters (keeping incall) in Burlington/Woburn and Newton so far.

You can get to tourist places in the city by subway. Revere beach is also accessable.

I would visit Back Bay, Beacon Hill, Quincy Market area, Seaport District and Fenway area.  As noted, Boston is a very walking friendly city and the subway system is very reliable and easy to use.

visit the North End, Charlestown, Jamica Plain, Hyde Park, Roxbury, Southie, West End, Back Bay & of course, Dorchesta.  At one time they were ethnically influenced, but now not so much.

Easy to manuver from there.  Casual mornings in the Common, easy walk to most of the city, including Newbury St., Fanuiel Hall and Copley Square.

Thank you everyone!