The first thing that comes to mind is one in South End:
Aquitaine - excellent food & wine list, may go a little over your 100$ mark
569 Tremont St
Boston, MA 02118
(617) 424-8577
Other places that would hit the mark, but aren't a Bistro are:
Sage, North End
69 Prince St, Boston, 02113 - (617) 248-8814
L'espalier - very expensive but out of this world, and in a fun area (Back Bay, off Newbury Street)
30 Gloucester Street, Boston, MA 02115 · 617 262 3023
#9 Park - also may be over your 100$ but well worth it.
9 Park St
Boston, MA 02108
(617) 742-9991
Sel De La Terre, on the waterfront
617 720 1300