Apartments.com has 0 rentals available in Brunswick. Trulia has one rental, a 3br house in the suburbs for $1450.
Eh, I guess. Never have lived in the cold before, so there’s really only one way to find out if I mind… 
In the Silicon Valley, you might have minimal expenses for heating and cooling your apartment, but it will almost certainly cost much more in the northeast, where the summers can be hot and humid (so that you may need air conditioning or at least fans) and the winters are cold (so that heating will be necessary).
Have you looked at cities in the interior of California? You might find a lower cost of living and a climate similar to what you’re used to.
Craigslist is the way to go for apartments anywhere in Maine.
The shortlist so far:
Boise, Idaho (41.0% lower COL)
Louisville, Kentucky (46.0% lower COL)
Memphis, Tennessee (50.3% lower COL)
St Louis, Missouri (44.8% lower COL)
Kansas City, Missouri/Kansas (42.7% lower COL)
Wichita, Kansas (47.8% lower COL)
Little Rock, Arkansas (42.6% lower COL)
Tucson, Arizona (41% lower COL)
One other factor will be health insurance premiums. I suppose with the ACA I can now expect fairly similar costs, but I can’t work out how to determine this, apart from using the healthcare.gov calculator with a zipcode from each of the above possibilities…
Brunswick, Maine, does have a lot going for it. And yes, Craigslist is where to find the open apts. HOWEVER, do not underestimate the effect of Maine weather on quality of life. I’ve never adjusted to it (after San Diego, so yeah, what was I thinking?) and it keeps me from enjoying much of the outdoor life from late Oct through mid-May.
If you want to be near a (smallish, but biggest here) city, try the smaller towns outside Portland. Rent in town here is pretty high for the area (say, 1500 for a nice 2-bd), but Westbrook, Gorham, South Portland are cheaper.
Have you checked Springfield Oregon? I’m looking at it myself–seems to offer alot–
Let me know if you have any questions about Memphis. The city gets a bad rap in the media sometimes, but it’s really pretty decent.
Hard to do better than Cleveland, OH and it’s first-ring suburbs for what you are looking for. Especially Lakewood, OH.
Chattanooga TN, has this, plus great scenery.
Philadelphia, the city I grew up in was famous for low rents and still is. The average rental cost is 84% of the national average. Even food is relatively cheap–relative to NY anyway, although slightly above the national average. The only thing that is out of sight is the cost of car insurance. Thanks to my cousin Jimmy who got rich from ambulance chasing.