I am looking for budget lodging in Boston. Ideal would be an accessable property near a subway/commuter rail with free parking. Need a room with 2 beds (2 adults, 2 kids).

My friends and I have stayed at the Best Western Roundhouse Suites. The rooms are fine. There is free outdoor parking next door and it is easy access from Rt 93 but some people have said they don't like the location. There is a free shuttle service to the T but it's also walkable (long walk). The continental breakfast was typical. We used cabs at night. The other downside is there isn't any great restaurants nearby. However, I like a room with a sitting area rather than the standard 2 double beds and one comfortable chair so that is a big plus for me. Also free parking is good.
We have never tried Priceline so possibly you can get a better hotel in a better location for less money.

How big is your 'budget'?
When do you intend to come?
Boston is cheaper in the winter!
The Marriott Courtyard South Boston is $149 a night at the moment and we often stay here before flying out of Logan (we've paid rates of $99, $109, $129inc. breakfast) over the last year.

The price rises the further out you book but we usually find a lower rate one to two weeks before our actual stay.

The hotels at the airport would match your needs. They have easy access to the Blue Line. Zero atmosphere in the immediate surroundings but safe enough.

You can try Priceline or Hotwire too.

I would avoid the Best Western - that area is truly sketchy.

We stayed at an Amerisuites near Boston, it was near two different subway stations with free parking and the hotel had free breakfast. I think it was in Milford...anyway it was the closest Amerisuites to Boston.

Amerisuites is Medford

Best Western New Englander in Woburn/Montvale might work for you...decent weekend rates for sure...shuttle to the train. Cost of Train might add up for 4 people round trip into town daily, however.