If you can find a hotel near any of these things you'll be easy walking distance to anything that matters in Boston:

Faneuil Hall, Aquarium, Financial District, Public Garden, Boston Common, Beacon Hill, Government Center, Old Statehouse, North End. There are many hotels around these areas that range from luxury (e.g. Four Seasons) to more traditional (e.g. Marriott).  Keep in mind that hotels in Boston tend to be expensive, so be prepared.

You could also stay in the Seaport District, which is a part of Boston which has really grown over the last 10 years.  It's still close to downtown, but you'll do a 10 minute walk to start/end your day.

The T (subway system) in Boston is great, and if you don't mind spending a little time getting to downtown, you can venture a little further afield (Newton, Cambridge, Watertown, etc.).  Stay away from anything in Roxbury, Jamaica Plain or Dorchester.