At the risk of being a kill joy I suspect that you won't be able to find anything that meets all of your criteria, unless your husband gets a regional cost of living salary increase and you can afford more than the $1,500 you are paying now.
Another poster up thread mentioned Rockland. I have a friend that lost the two bedroom rental she was paying $1,200 a month for; and it was in rough shape. I guesstimate it had about half an acre of land which she didn't want or need. She couldn't find any apartment --let alone a house with land-- in that price range. Ultimately she moved to Fall River which is about 45 minutes to an hour from Rockland.
Another poster mentioned that traffic around Quincy can be tough, that's an understatement. Although it's a small city, it's still a city and bad weather or street repairs can slow you down considerably. To give you some idea, I live in a town a little south of Quincy and have been taking a class two towns west of Quincy. According to Mapquest it's about 9 miles from my house and should take about 15 minutes to get there. Of course the highway traffic during rush hour is brutal so I've been taking the back roads through Quincy. I quickly learned that the most direct back road route took as long or longer than the highway. The alternate route worked pretty well for the first couple of weeks, until they started with road repairs on a busy secondary road leading from Quincy to Milton. Now it takes more like 40 to 45 minutes.
If you know the street address for the Quincy office I would suggest checking out Realtor.com or Zillow for rentals in the Weymouth / Rockland area and randomly pick a property and try Mapquesting or Google mapping it to give you some idea of how long the commute would be in non rush hour traffic and then multiply by 2 or 2 1/2.
I've included some links below.
City of Quincy
City Data - Quincy
Land area: 16.8 square miles
Population density: 5542 people per square mile