The best online search engine for finding and booking hotels in the Boston area is KAYAK. You will get significantly better rates through KAYAK than you would by contacting the hotels directly.
 
Here are some recommended budget hotels near Harvard Square.
 
Best Western TLC Hotel
380 Winter Street,
477 Totten Pond Road
Waltham, MA
Phone: (781) 890-7800 
Phone: 1-800-780-7234
website

$79/night plus tax (online or phone bookings)
 
14 mile from Harvard Square.
Free on site parking.
Not accessible by public transportation.
 
 

Courtyard by Marriott Woburn
240 Mishawum Road
Woburn, MA 01801
Phone:  (781) 932-3200
website
 
$84/night plus tax (online or phone bookings)
 
13 miles/25 minute drive from Harvard Square.
Free on site parking.
Not accessible by public transportation.
 
 
 
La Quinta Inn & Suites
23 Cummings Street
Somerville, MA 02145
Phone: (617) 625-5300
website
 
 
$84-$94/night plus tax if you book online through their website
$119/night plus tax if you call

5 miles/8 minute drive from Harvard Square.
Free on site parking.
Not easily accessible by public transportation.
 
 
Royal Sonesta Hotel Boston
40 Edwin Land Boulevard
Cambridge, MA 02142
Phone: (617) 806-4200
website
 
$129-$139/night plus tax if you book through KAYAK
 
Will have to pay extra for parking ($25.00 per night).
Accessible by public transportation. Bus number 69 will take you directly from the Cambridge Galleria where the Sonesta is located to Harvard Square.
Complementary shuttle service to Harvard Square (every 3 hours).